Edit Profile Hofmann, Steve Compute Distance To: Compute Author ID: hofmann.steve Published as: Hofmann, Steve; Hofmann, S.; Hofmann, Steven External Links: MGP · Wikidata · GND Documents Indexed: 107 Publications since 1988, including 3 Books all top 5 Co-Authors 21 single-authored 19 Martell, José María (Chema) 14 Mayboroda, Svitlana 12 Lewis, John L. 11 Mitrea, Marius 9 Auscher, Pascal 7 McIntosh, Alan 5 Bortz, Simon 5 Nyström, Kaj 4 Azzam, Jonas 4 Barton, Ariel 4 Mitrea, Dorina 4 Morris, Andrew Joel 4 Mourgoglou, Mihalis 4 Taylor, Michael Eugene 4 Tchamitchian, Philippe 4 Toro, Tatiana 3 Gesztesy, Fritz 3 Iosevich, Alex 3 Kim, Seick 3 Lacey, Michael T. 3 Le, Phi Long 3 Nichols, Roger 3 Tolsa, Xavier 2 Akman, Murat 2 Axelsson, Andreas 2 Cavero, Juan 2 Duong, Xuan Thinh 2 Genschaw, Alyssa 2 Grau de la Herrán, Ana 2 Kenig, Carlos Eduardo 2 Pipher, Jill Catherine 2 Tapiola, Olli 2 Volberg, Alexander Lvovich 2 Yan, Lixin 1 Alfonseca-Cubero, María de los Ángeles 1 Badger, Matthew 1 Brandolini, Luca 1 Carbery, Anthony 1 Chen, Yanping 1 Coulhon, Thierry 1 Ding, Yong 1 Escauriaza Zubiria, Luis 1 Li, Xinwei 1 Lu, Guozhen 1 Luna, José Luis 1 Marmolejo-Olea, Emilio 1 Monniaux, Sylvie 1 Muscalu, Camil 1 Pérez-Esteva, Salvador 1 Tao, Terence 1 Thiele, Christoph Martin 1 Uriarte-Tuero, Ignacio 1 Weidinger, D. 1 Wright, James Robert 1 Yang, Dachun 1 Zhang, Guoming 1 Zhao, Zihui all top 5 Serials 8 Proceedings of the American Mathematical Society 6 Transactions of the American Mathematical Society 4 Duke Mathematical Journal 4 Revista Matemática Iberoamericana 4 Publicacions Matemàtiques 4 Geometric and Functional Analysis. GAFA 3 Advances in Mathematics 3 Annales de l’Institut Fourier 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Journal of Functional Analysis 3 Mathematische Annalen 3 Memoirs of the American Mathematical Society 3 Proceedings of the London Mathematical Society. Third Series 3 The Journal of Geometric Analysis 3 Annals of Mathematics. Second Series 3 Analysis & PDE 2 Studia Mathematica 2 Illinois Journal of Mathematics 2 Journal of Differential Equations 2 Mathematika 2 IMRN. International Mathematics Research Notices 2 Potential Analysis 2 Acta Mathematica Sinica. English Series 1 Journal of Mathematical Analysis and Applications 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Arkiv för Matematik 1 Acta Mathematica 1 Canadian Mathematical Bulletin 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Michigan Mathematical Journal 1 Journal of the American Mathematical Society 1 Methods and Applications of Analysis 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Methods of Functional Analysis and Topology 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Evolution Equations 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Electronic Research Announcements in Mathematical Sciences 1 Bulletin of Mathematical Sciences all top 5 Fields 73 Harmonic analysis on Euclidean spaces (42-XX) 65 Partial differential equations (35-XX) 28 Potential theory (31-XX) 19 Operator theory (47-XX) 13 Measure and integration (28-XX) 7 Functional analysis (46-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Functions of a complex variable (30-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 92 Publications have been cited 1,785 times in 873 Documents Cited by ▼ Year ▼ The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\). Zbl 1128.35316Auscher, Pascal; Hofmann, Steve; Lacey, Michael; McIntosh, Alan; Tchamitchian, Ph. 146 2002 Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Zbl 1232.42018Hofmann, Steve; Lu, Guozhen; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin 134 2011 Hardy and BMO spaces associated to divergence form elliptic operators. Zbl 1162.42012Hofmann, Steve; Mayboroda, Svitlana 133 2009 Riesz transform on manifolds and heat kernel regularity. Zbl 1086.58013Auscher, Pascal; Coulhon, Thierry; Duong, Xuan Thinh; Hofmann, Steve 116 2004 Second order elliptic operators with complex bounded measurable coefficients in \(L^p\), Sobolev and Hardy spaces. (Opérateurs elliptiques du second ordre à coefficients complexes mesurables bornés dans les espaces \(L^p\), de Sobolev et de Hardy.) Zbl 1243.47072Hofmann, Steve; Mayboroda, Svitlana; McIntosh, Alan 66 2011 \(L^p\) bounds for Riesz transforms and square roots associated to second order elliptic operators. Zbl 1074.35031Hofmann, Steve; Martell, José María 61 2003 Analyticity of layer potentials and \(L^{2}\) solvability of boundary value problems for divergence form elliptic equations with complex \(L^{\infty }\) coefficients. Zbl 1217.35056Alfonseca, M. Angeles; Auscher, Pascal; Axelsson, Andreas; Hofmann, Steve; Kim, Seick 55 2011 The Green function estimates for strongly elliptic systems of second order. Zbl 1130.35042Hofmann, Steve; Kim, Seick 55 2007 Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators. Zbl 1326.42028Hofmann, Steve; Kenig, Carlos; Mayboroda, Svitlana; Pipher, Jill 42 2015 Singular integrals and elliptic boundary problems on regular Semmes-Kenig-Toro. Zbl 1221.31010Hofmann, Steve; Mitrea, Marius; Taylor, Michael 41 2010 Carleson measures, trees, extrapolation, and \(T(b)\) theorems. Zbl 1027.42009Auscher, P.; Hofmann, S.; Muscalu, Camil; Tao, Terence C.; Thiele, Christoph 40 2002 Uniform rectifiability and harmonic measure. I: Uniform rectifiability implies Poisson kernels in \(L^p\). (Uniforme rectifiabilité et mesure harmonique. I: L’uniforme rectifiabilité entraine le noyau de Poisson dans \(L^p\).) Zbl 1302.31007Hofmann, Steve; Martell, José María 35 2014 \(L^ 2\) solvability and representation by caloric layer potentials in time-varying domains. Zbl 0867.35037Hofmann, Steve; Lewis, John L. 35 1996 Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains. Zbl 1142.49021Hofmann, Steve; Mitrea, Marius; Taylor, Michael 34 2007 The Kato square root problem for higher order elliptic operators and systems on \(\mathbb{R}^n\). Zbl 1019.35029Auscher, Pascal; Hofmann, Steve; McIntosh, Alan; Tchamitchian, Philippe 33 2001 Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems. Zbl 1157.35028Auscher, Pascal; Axelsson, Andreas; Hofmann, Steve 31 2008 A new characterization of chord-arc domains. Zbl 1366.28004Azzam, Jonas; Hofmann, Steve; Martell, José María; Nyström, Kaj; Toro, Tatiana 28 2017 Extrapolation of Carleson measures and the analyticity of Kato’s square-root operators. Zbl 1163.35346Auscher, Pascal; Hofmann, Steve; Lewis, John L.; Tchamitchian, Philippe 27 2001 Rectifiability of harmonic measure. Zbl 1354.31004Azzam, Jonas; Hofmann, Steve; Martell, José María; Mayboroda, Svitlana; Mourgoglou, Mihalis; Tolsa, Xavier; Volberg, Alexander 27 2016 The Dirichlet problem for parabolic operators with singular drift terms. Zbl 1149.35048Hofmann, Steve; Lewis, John L. 26 2001 Uniform rectifiability and harmonic measure. II: Poisson kernels in \(L^p\) imply uniform rectifiability. Zbl 1323.31008Hofmann, Steve; Martell, José María; Uriarte-Tuero, Ignacio 26 2014 Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems. Zbl 1263.35080Duong, Xuan Thinh; Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin 25 2013 The solution of the Kato problem for divergence from elliptic operators with Gaussian heat kernel bounds. Zbl 1128.35317Hofmann, Steve; Lacey, Michael; McIntosh, Alan 25 2002 Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials. Zbl 0941.42006Hofmann, Steve 23 1997 Weighted norm inequalities and vector valued inequalities for certain rough operators. Zbl 0804.42010Hofmann, Steve 22 1993 The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients. Zbl 1325.42028Hofmann, Steve; Kenig, Carlos; Mayboroda, Svitlana; Pipher, Jill 22 2015 Sharp rate of average decay of the Fourier transform of a bounded set. Zbl 1032.42017Brandolini, L.; Hofmann, S.; Iosevich, A. 21 2003 Layer potentials and boundary value problems for elliptic equations with complex \(L^\infty\) coefficients satisfying the small Carleson measure norm condition. Zbl 1311.35074Hofmann, Steve; Mayboroda, Svitlana; Mourgoglou, Mihalis 20 2015 The method of layer potentials in \(L^{p}\) and endpoint spaces for elliptic operators with \(L^{\infty}\) coefficients. Zbl 1323.31011Hofmann, Steve; Mitrea, Marius; Morris, Andrew J. 20 2015 Caloric measure in parabolic flat domains. Zbl 1074.35041Hofmann, Steve; Lewis, John L.; Nyström, Kaj 19 2004 Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions. Zbl 1359.28005Hofmann, Steve; Martell, José María; Mayboroda, Svitlana 19 2016 Vertical versus conical square functions. Zbl 1275.42028Auscher, Pascal; Hofmann, Steve; Martell, José-María 18 2012 On certain nonstandard Calderón-Zygmund operators. Zbl 0826.42012Hofmann, Steve 18 1994 The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability. Zbl 1369.31006Hofmann, Steve; Le, Phi; Martell, José María; Nyström, Kaj 17 2017 Gaussian estimates for fundamental solutions to certain parabolic systems. Zbl 1061.35023Hofmann, Steve; Kim, Seick 16 2004 The solution of the Kato problem in two dimensions. Zbl 1020.47031Hofmann, Steve; McIntosh, Alan 16 2002 Circular averages and Falconer/Erdős distance conjecture in the plane for random metrics. Zbl 1096.28004Hofmann, S.; Iosevich, A. 15 2005 Weak (1,1) boundedness of singular integrals with nonsmooth kernel. Zbl 0677.42013Hofmann, Steve 13 1988 \(L^p\)-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets. Zbl 1371.28004Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Morris, Andrew J. 13 2016 A local \(Tb\) theorem for square functions. Zbl 1156.42307Hofmann, Steve 12 2008 \(A_\infty\) implies NTA for a class of variable coefficient elliptic operators. Zbl 1378.35092Hofmann, Steve; Martell, José María; Toro, Tatiana 12 2017 Hardy spaces, singular integrals and the geometry of Euclidean domains of locally finite perimeter. Zbl 1333.42020Hofmann, Steve; Marmolejo-Olea, Emilio; Mitrea, Marius; Pérez-Esteva, Salvador; Taylor, Michael 11 2009 Uniform rectifiability and harmonic measure. III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains. Zbl 1305.31005Hofmann, Steve; Martell, José María; Mayboroda, Svitlana 11 2014 \(T1\) theorems for Besov and Triebel-Lizorkin spaces. Zbl 0779.42010Han, Y.-S.; Hofmann, Steve 11 1993 The \(L^p\) Neumann problem for the heat equation in non-cylindrical domains. Zbl 1065.35125Hofmann, Steve; Lewis, John L. 10 2005 Existence of big pieces of graphs for parabolic problems. Zbl 1046.35045Hofmann, Steve; Lewis, John L.; Nyström, Kaj 10 2003 Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries. Zbl 1373.31003Akman, Murat; Badger, Matthew; Hofmann, Steve; Martell, José María 10 2017 Boundedness and applications of singular integrals and square functions: a survey. Zbl 1255.42016Hofmann, Steve; Mcintosh, Alan 8 2011 The solution of Kato’s conjectures. Zbl 1017.47034Auscher, Pascal; Hofmann, Steve; Lacey, Michael; Lewis, John; McIntosh, Alan; Tchamitchian, Philippe 8 2001 On singular integrals of Calderón-type in \(\mathbb{R}^ n\), and BMO. Zbl 0874.42011Hofmann, Steve 7 1994 Square functions of Calderón type and applications. Zbl 0980.42011Hofmann, Steve; Lewis, John L. 7 2001 Local \(Tb\) theorems and applications in PDE. Zbl 1104.42007Hofmann, Steve 6 2006 Symbol calculus for operators of layer potential type on Lipschitz surfaces with VMO normals, and related pseudodifferential operator calculus. Zbl 1317.31012Hofmann, Steve; Mitrea, Marius; Taylor, Michael E. 6 2015 BMO solvability and absolute continuity of harmonic measure. Zbl 1405.42032Hofmann, Steve; Le, Phi 6 2018 Dahlberg’s bilinear estimate for solutions of divergence form complex elliptic equations. Zbl 1172.42006Hofmann, Steve 5 2008 A note on \(A_\infty\) estimates via extrapolation of Carleson measures. Zbl 1228.42023Hofmann, Steve; Martell, José María 5 2010 \(A_{\infty }\) estimates via extrapolation of Carleson measures and applications to divergence form elliptic operators. Zbl 1247.42020Hofmann, Steve; Martell, José María 5 2012 An off-diagonal \(T1\) theorem and applications. Zbl 0919.42012Hofmann, Steve 5 1998 A characterization of commutators of parabolic singular integrals. Zbl 1039.42500Hofmann, Steve 5 1995 Boundedness criteria for rough singular integrals. Zbl 0831.42011Hofmann, Steve 5 1995 Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains. Zbl 1036.35067Hofmann, Steve; Lewis, John; Mitrea, Marius 5 2003 Square function estimates on layer potentials for higher-order elliptic equations. Zbl 1381.35035Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana 5 2017 Rectifiability, interior approximation and harmonic measure. Zbl 1423.31002Akman, Murat; Bortz, Simon; Hofmann, Steve; Martell, José María 4 2019 Local \(T(b)\) theorems and applications in PDE. Zbl 1204.42023Hofmann, Steve 4 2010 The \(L^p\) regularity problem for the heat equation in non-cylindrical domains. Zbl 0934.35056Hofmann, Steven; Lewis, John L. 4 1999 Generalized local \(Tb\) theorems for square functions. Zbl 1366.42022Grau de la Herrán, Ana; Hofmann, Steve 4 2017 Harmonic measure and approximation of uniformly rectifiable sets. Zbl 1371.28002Bortz, Simon; Hofmann, Steve 4 2017 The Neumann problem for higher order elliptic equations with symmetric coefficients. Zbl 1394.35159Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana 4 2018 Harmonic measure and quantitative connectivity: geometric characterization of the \(L^p\)-solvability of the Dirichlet problem. Zbl 1453.31009Azzam, Jonas; Hofmann, Steve; Martell, José María; Mourgoglou, Mihalis; Tolsa, Xavier 4 2020 Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds. Zbl 1239.42013Hofmann, Steve; Mitrea, Marius; Monniaux, Sylvie 3 2011 Dirichlet problems for a nonstationary linearized system of Navier-Stokes equations in non-cylindrical domains. Zbl 1057.35030Hofmann, Steve; Nyström, Kaj 3 2002 Weighted weak-type (1,1) inequalities for rough operators. Zbl 0694.42024Hofmann, Steve 3 1989 Singular integrals with power weights. Zbl 0717.42018Hofmann, Steve 3 1990 A singular integral approach to a two phase free boundary problem. Zbl 1361.42012Bortz, Simon; Hofmann, Steve 3 2016 A local \(Tb\) theorem with vector-valued testing functions. Zbl 1345.42012Grau de la Herrán, Ana; Hofmann, Steve 3 2016 Perturbations of elliptic operators in 1-sided chord-arc domains. II: Non-symmetric operators and Carleson measure estimates. Zbl 1453.31011Cavero, Juan; Hofmann, Steve; Martell, José María; Toro, Tatiana 3 2020 Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress. Zbl 1421.31010Hofmann, Steve 3 2019 The commutator of the Kato square root for second order elliptic operators on \(\mathbb{R}^n\). Zbl 1351.42027Chen, Yan Ping; Ding, Yong; Hofmann, Steve 3 2016 On stability of square root domains for non-self-adjoint operators under additive perturbations. Zbl 1345.47015Gesztesy, Fritz; Hofmann, Steve; Nichols, Roger 2 2016 Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains. Zbl 1308.35082Gesztesy, Fritz; Hofmann, Steve; Nichols, Roger 2 2015 The Calderón commutator along a parabola. Zbl 0948.42009Carbery, Anthony; Hofmann, Steve; Wright, James 2 1999 A short course on the Kato problem. Zbl 1012.47013Hofmann, Steve 2 2001 Lattice points inside random ellipsoids. Zbl 1056.11052Hofmann, S.; Iosevich, A.; Weidinger, D. 2 2004 Perturbations of elliptic operators in 1-sided chord-arc domains. I: Small and large perturbation for symmetric operators. Zbl 1410.31003Cavero, Juan; Hofmann, Steve; Martell, José María 2 2019 A weak reverse Hölder inequality for caloric measure. Zbl 1436.42028Genschaw, Alyssa; Hofmann, Steve 2 2020 Uniform rectifiability and \(\varepsilon\)-approximability of harmonic functions in \(L^p\). (Rectifiabilité uniforme et \(\varepsilon\)-approximation dans \(L^p\).) Zbl 1465.42024Hofmann, Steve; Tapiola, Olli 2 2020 Dirichlet and Neumann boundary values of solutions to higher order elliptic equations. (Conditions aux limites de type Dirichlet ou Neumann non-homogènes pour les solutions d’équations elliptiques d’ordre supérieur.) Zbl 1432.35091Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana 1 2019 A generalized characterization of commutators of parabolic singular integrals. Zbl 0953.42008Hofmann, Steve; Li, Xinwei; Yang, Dachun 1 1999 A weak molecule condition for certain Triebel-Lizorkin spaces. Zbl 0811.46025Hofmann, Steve 1 1992 Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets. Zbl 1286.28003Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Morris, Andrew J. 1 2014 Kato square root problem with unbounded leading coefficients. Zbl 1400.35041Escauriaza, Luis; Hofmann, Steve 1 2018 Quantitative Fatou theorems and uniform rectifiability. Zbl 1453.31010Bortz, Simon; Hofmann, Steve 1 2020 Harmonic measure and quantitative connectivity: geometric characterization of the \(L^p\)-solvability of the Dirichlet problem. Zbl 1453.31009Azzam, Jonas; Hofmann, Steve; Martell, José María; Mourgoglou, Mihalis; Tolsa, Xavier 4 2020 Perturbations of elliptic operators in 1-sided chord-arc domains. II: Non-symmetric operators and Carleson measure estimates. Zbl 1453.31011Cavero, Juan; Hofmann, Steve; Martell, José María; Toro, Tatiana 3 2020 A weak reverse Hölder inequality for caloric measure. Zbl 1436.42028Genschaw, Alyssa; Hofmann, Steve 2 2020 Uniform rectifiability and \(\varepsilon\)-approximability of harmonic functions in \(L^p\). (Rectifiabilité uniforme et \(\varepsilon\)-approximation dans \(L^p\).) Zbl 1465.42024Hofmann, Steve; Tapiola, Olli 2 2020 Quantitative Fatou theorems and uniform rectifiability. Zbl 1453.31010Bortz, Simon; Hofmann, Steve 1 2020 Rectifiability, interior approximation and harmonic measure. Zbl 1423.31002Akman, Murat; Bortz, Simon; Hofmann, Steve; Martell, José María 4 2019 Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress. Zbl 1421.31010Hofmann, Steve 3 2019 Perturbations of elliptic operators in 1-sided chord-arc domains. I: Small and large perturbation for symmetric operators. Zbl 1410.31003Cavero, Juan; Hofmann, Steve; Martell, José María 2 2019 Dirichlet and Neumann boundary values of solutions to higher order elliptic equations. (Conditions aux limites de type Dirichlet ou Neumann non-homogènes pour les solutions d’équations elliptiques d’ordre supérieur.) Zbl 1432.35091Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana 1 2019 BMO solvability and absolute continuity of harmonic measure. Zbl 1405.42032Hofmann, Steve; Le, Phi 6 2018 The Neumann problem for higher order elliptic equations with symmetric coefficients. Zbl 1394.35159Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana 4 2018 Kato square root problem with unbounded leading coefficients. Zbl 1400.35041Escauriaza, Luis; Hofmann, Steve 1 2018 A new characterization of chord-arc domains. Zbl 1366.28004Azzam, Jonas; Hofmann, Steve; Martell, José María; Nyström, Kaj; Toro, Tatiana 28 2017 The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability. Zbl 1369.31006Hofmann, Steve; Le, Phi; Martell, José María; Nyström, Kaj 17 2017 \(A_\infty\) implies NTA for a class of variable coefficient elliptic operators. Zbl 1378.35092Hofmann, Steve; Martell, José María; Toro, Tatiana 12 2017 Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries. Zbl 1373.31003Akman, Murat; Badger, Matthew; Hofmann, Steve; Martell, José María 10 2017 Square function estimates on layer potentials for higher-order elliptic equations. Zbl 1381.35035Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana 5 2017 Generalized local \(Tb\) theorems for square functions. Zbl 1366.42022Grau de la Herrán, Ana; Hofmann, Steve 4 2017 Harmonic measure and approximation of uniformly rectifiable sets. Zbl 1371.28002Bortz, Simon; Hofmann, Steve 4 2017 Rectifiability of harmonic measure. Zbl 1354.31004Azzam, Jonas; Hofmann, Steve; Martell, José María; Mayboroda, Svitlana; Mourgoglou, Mihalis; Tolsa, Xavier; Volberg, Alexander 27 2016 Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions. Zbl 1359.28005Hofmann, Steve; Martell, José María; Mayboroda, Svitlana 19 2016 \(L^p\)-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets. Zbl 1371.28004Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Morris, Andrew J. 13 2016 A singular integral approach to a two phase free boundary problem. Zbl 1361.42012Bortz, Simon; Hofmann, Steve 3 2016 A local \(Tb\) theorem with vector-valued testing functions. Zbl 1345.42012Grau de la Herrán, Ana; Hofmann, Steve 3 2016 The commutator of the Kato square root for second order elliptic operators on \(\mathbb{R}^n\). Zbl 1351.42027Chen, Yan Ping; Ding, Yong; Hofmann, Steve 3 2016 On stability of square root domains for non-self-adjoint operators under additive perturbations. Zbl 1345.47015Gesztesy, Fritz; Hofmann, Steve; Nichols, Roger 2 2016 Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators. Zbl 1326.42028Hofmann, Steve; Kenig, Carlos; Mayboroda, Svitlana; Pipher, Jill 42 2015 The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients. Zbl 1325.42028Hofmann, Steve; Kenig, Carlos; Mayboroda, Svitlana; Pipher, Jill 22 2015 Layer potentials and boundary value problems for elliptic equations with complex \(L^\infty\) coefficients satisfying the small Carleson measure norm condition. Zbl 1311.35074Hofmann, Steve; Mayboroda, Svitlana; Mourgoglou, Mihalis 20 2015 The method of layer potentials in \(L^{p}\) and endpoint spaces for elliptic operators with \(L^{\infty}\) coefficients. Zbl 1323.31011Hofmann, Steve; Mitrea, Marius; Morris, Andrew J. 20 2015 Symbol calculus for operators of layer potential type on Lipschitz surfaces with VMO normals, and related pseudodifferential operator calculus. Zbl 1317.31012Hofmann, Steve; Mitrea, Marius; Taylor, Michael E. 6 2015 Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains. Zbl 1308.35082Gesztesy, Fritz; Hofmann, Steve; Nichols, Roger 2 2015 Uniform rectifiability and harmonic measure. I: Uniform rectifiability implies Poisson kernels in \(L^p\). (Uniforme rectifiabilité et mesure harmonique. I: L’uniforme rectifiabilité entraine le noyau de Poisson dans \(L^p\).) Zbl 1302.31007Hofmann, Steve; Martell, José María 35 2014 Uniform rectifiability and harmonic measure. II: Poisson kernels in \(L^p\) imply uniform rectifiability. Zbl 1323.31008Hofmann, Steve; Martell, José María; Uriarte-Tuero, Ignacio 26 2014 Uniform rectifiability and harmonic measure. III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains. Zbl 1305.31005Hofmann, Steve; Martell, José María; Mayboroda, Svitlana 11 2014 Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets. Zbl 1286.28003Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Morris, Andrew J. 1 2014 Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems. Zbl 1263.35080Duong, Xuan Thinh; Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin 25 2013 Vertical versus conical square functions. Zbl 1275.42028Auscher, Pascal; Hofmann, Steve; Martell, José-María 18 2012 \(A_{\infty }\) estimates via extrapolation of Carleson measures and applications to divergence form elliptic operators. Zbl 1247.42020Hofmann, Steve; Martell, José María 5 2012 Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Zbl 1232.42018Hofmann, Steve; Lu, Guozhen; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin 134 2011 Second order elliptic operators with complex bounded measurable coefficients in \(L^p\), Sobolev and Hardy spaces. (Opérateurs elliptiques du second ordre à coefficients complexes mesurables bornés dans les espaces \(L^p\), de Sobolev et de Hardy.) Zbl 1243.47072Hofmann, Steve; Mayboroda, Svitlana; McIntosh, Alan 66 2011 Analyticity of layer potentials and \(L^{2}\) solvability of boundary value problems for divergence form elliptic equations with complex \(L^{\infty }\) coefficients. Zbl 1217.35056Alfonseca, M. Angeles; Auscher, Pascal; Axelsson, Andreas; Hofmann, Steve; Kim, Seick 55 2011 Boundedness and applications of singular integrals and square functions: a survey. Zbl 1255.42016Hofmann, Steve; Mcintosh, Alan 8 2011 Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds. Zbl 1239.42013Hofmann, Steve; Mitrea, Marius; Monniaux, Sylvie 3 2011 Singular integrals and elliptic boundary problems on regular Semmes-Kenig-Toro. Zbl 1221.31010Hofmann, Steve; Mitrea, Marius; Taylor, Michael 41 2010 A note on \(A_\infty\) estimates via extrapolation of Carleson measures. Zbl 1228.42023Hofmann, Steve; Martell, José María 5 2010 Local \(T(b)\) theorems and applications in PDE. Zbl 1204.42023Hofmann, Steve 4 2010 Hardy and BMO spaces associated to divergence form elliptic operators. Zbl 1162.42012Hofmann, Steve; Mayboroda, Svitlana 133 2009 Hardy spaces, singular integrals and the geometry of Euclidean domains of locally finite perimeter. Zbl 1333.42020Hofmann, Steve; Marmolejo-Olea, Emilio; Mitrea, Marius; Pérez-Esteva, Salvador; Taylor, Michael 11 2009 Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems. Zbl 1157.35028Auscher, Pascal; Axelsson, Andreas; Hofmann, Steve 31 2008 A local \(Tb\) theorem for square functions. Zbl 1156.42307Hofmann, Steve 12 2008 Dahlberg’s bilinear estimate for solutions of divergence form complex elliptic equations. Zbl 1172.42006Hofmann, Steve 5 2008 The Green function estimates for strongly elliptic systems of second order. Zbl 1130.35042Hofmann, Steve; Kim, Seick 55 2007 Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains. Zbl 1142.49021Hofmann, Steve; Mitrea, Marius; Taylor, Michael 34 2007 Local \(Tb\) theorems and applications in PDE. Zbl 1104.42007Hofmann, Steve 6 2006 Circular averages and Falconer/Erdős distance conjecture in the plane for random metrics. Zbl 1096.28004Hofmann, S.; Iosevich, A. 15 2005 The \(L^p\) Neumann problem for the heat equation in non-cylindrical domains. Zbl 1065.35125Hofmann, Steve; Lewis, John L. 10 2005 Riesz transform on manifolds and heat kernel regularity. Zbl 1086.58013Auscher, Pascal; Coulhon, Thierry; Duong, Xuan Thinh; Hofmann, Steve 116 2004 Caloric measure in parabolic flat domains. Zbl 1074.35041Hofmann, Steve; Lewis, John L.; Nyström, Kaj 19 2004 Gaussian estimates for fundamental solutions to certain parabolic systems. Zbl 1061.35023Hofmann, Steve; Kim, Seick 16 2004 Lattice points inside random ellipsoids. Zbl 1056.11052Hofmann, S.; Iosevich, A.; Weidinger, D. 2 2004 \(L^p\) bounds for Riesz transforms and square roots associated to second order elliptic operators. Zbl 1074.35031Hofmann, Steve; Martell, José María 61 2003 Sharp rate of average decay of the Fourier transform of a bounded set. Zbl 1032.42017Brandolini, L.; Hofmann, S.; Iosevich, A. 21 2003 Existence of big pieces of graphs for parabolic problems. Zbl 1046.35045Hofmann, Steve; Lewis, John L.; Nyström, Kaj 10 2003 Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains. Zbl 1036.35067Hofmann, Steve; Lewis, John; Mitrea, Marius 5 2003 The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\). Zbl 1128.35316Auscher, Pascal; Hofmann, Steve; Lacey, Michael; McIntosh, Alan; Tchamitchian, Ph. 146 2002 Carleson measures, trees, extrapolation, and \(T(b)\) theorems. Zbl 1027.42009Auscher, P.; Hofmann, S.; Muscalu, Camil; Tao, Terence C.; Thiele, Christoph 40 2002 The solution of the Kato problem for divergence from elliptic operators with Gaussian heat kernel bounds. Zbl 1128.35317Hofmann, Steve; Lacey, Michael; McIntosh, Alan 25 2002 The solution of the Kato problem in two dimensions. Zbl 1020.47031Hofmann, Steve; McIntosh, Alan 16 2002 Dirichlet problems for a nonstationary linearized system of Navier-Stokes equations in non-cylindrical domains. Zbl 1057.35030Hofmann, Steve; Nyström, Kaj 3 2002 The Kato square root problem for higher order elliptic operators and systems on \(\mathbb{R}^n\). Zbl 1019.35029Auscher, Pascal; Hofmann, Steve; McIntosh, Alan; Tchamitchian, Philippe 33 2001 Extrapolation of Carleson measures and the analyticity of Kato’s square-root operators. Zbl 1163.35346Auscher, Pascal; Hofmann, Steve; Lewis, John L.; Tchamitchian, Philippe 27 2001 The Dirichlet problem for parabolic operators with singular drift terms. Zbl 1149.35048Hofmann, Steve; Lewis, John L. 26 2001 The solution of Kato’s conjectures. Zbl 1017.47034Auscher, Pascal; Hofmann, Steve; Lacey, Michael; Lewis, John; McIntosh, Alan; Tchamitchian, Philippe 8 2001 Square functions of Calderón type and applications. Zbl 0980.42011Hofmann, Steve; Lewis, John L. 7 2001 A short course on the Kato problem. Zbl 1012.47013Hofmann, Steve 2 2001 The \(L^p\) regularity problem for the heat equation in non-cylindrical domains. Zbl 0934.35056Hofmann, Steven; Lewis, John L. 4 1999 The Calderón commutator along a parabola. Zbl 0948.42009Carbery, Anthony; Hofmann, Steve; Wright, James 2 1999 A generalized characterization of commutators of parabolic singular integrals. Zbl 0953.42008Hofmann, Steve; Li, Xinwei; Yang, Dachun 1 1999 An off-diagonal \(T1\) theorem and applications. Zbl 0919.42012Hofmann, Steve 5 1998 Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials. Zbl 0941.42006Hofmann, Steve 23 1997 \(L^ 2\) solvability and representation by caloric layer potentials in time-varying domains. Zbl 0867.35037Hofmann, Steve; Lewis, John L. 35 1996 A characterization of commutators of parabolic singular integrals. Zbl 1039.42500Hofmann, Steve 5 1995 Boundedness criteria for rough singular integrals. Zbl 0831.42011Hofmann, Steve 5 1995 On certain nonstandard Calderón-Zygmund operators. Zbl 0826.42012Hofmann, Steve 18 1994 On singular integrals of Calderón-type in \(\mathbb{R}^ n\), and BMO. Zbl 0874.42011Hofmann, Steve 7 1994 Weighted norm inequalities and vector valued inequalities for certain rough operators. Zbl 0804.42010Hofmann, Steve 22 1993 \(T1\) theorems for Besov and Triebel-Lizorkin spaces. Zbl 0779.42010Han, Y.-S.; Hofmann, Steve 11 1993 A weak molecule condition for certain Triebel-Lizorkin spaces. Zbl 0811.46025Hofmann, Steve 1 1992 Singular integrals with power weights. Zbl 0717.42018Hofmann, Steve 3 1990 Weighted weak-type (1,1) inequalities for rough operators. Zbl 0694.42024Hofmann, Steve 3 1989 Weak (1,1) boundedness of singular integrals with nonsmooth kernel. Zbl 0677.42013Hofmann, Steve 13 1988 all cited Publications top 5 cited Publications all top 5 Cited by 702 Authors 53 Hofmann, Steve 48 Yang, Dachun 32 Duong, Xuan Thinh 32 Yan, Lixin 31 Auscher, Pascal 31 Mitrea, Marius 28 Martell, José María (Chema) 24 Mayboroda, Svitlana 24 Mourgoglou, Mihalis 22 The Anh Bui 20 Ding, Yong 20 Yang, Sibei 19 Li, Ji 19 Nyström, Kaj 18 Song, Liang 16 Kim, Seick 15 McIntosh, Alan 15 Pipher, Jill Catherine 14 Mitrea, Irina 14 Tolsa, Xavier 13 Bernicot, Frédéric 13 Chen, Yanping 13 Jiang, Renjin 13 Kenig, Carlos Eduardo 12 Azzam, Jonas 12 Dindoš, Martin 11 Cao, Jun 11 Mitrea, Dorina 10 Frey, Dorothee 9 Barton, Ariel 9 Coulhon, Thierry 9 Iosevich, Alex 9 Martikainen, Henri 9 Portal, Pierre 9 Shen, Zhongwei 9 Toro, Tatiana 8 Betancor Perez, Jorge Juan 8 Chen, Peng 8 Dong, Hongjie 8 Gong, Ruming 8 Lewis, John L. 7 Badr, Nadine 7 Chang, Tongkeun 7 Egert, Moritz 7 Hytönen, Tuomas P. 7 Kohr, Mirela 7 Monniaux, Sylvie 7 Ouhabaz, El Maati 7 Wendland, Wolfgang L. 6 Axelsson, Andreas 6 Bandara, Lashi 6 Chang, Der-Chen E. 6 Choi, Jongkeun 6 David, Guy 6 Dziubański, Jacek 6 Feneuil, Joseph 6 Hassell, Andrew 6 Huang, Jizheng 6 Kunstmann, Peer Christian 6 Li, Pengtao 6 Liu, Suying 6 Liu, Yu 6 Morris, Andrew Joel 6 Rivera-Noriega, Jorge 6 Rodríguez-Mesa, Lourdes 6 Russ, Emmanuel 6 van Neerven, Jan M. A. M. 6 Zhuo, Ciqiang 5 Baudoin, Fabrice 5 Bortz, Simon 5 Chen, Jiecheng 5 Devyver, Baptiste 5 Gesztesy, Fritz 5 Kheloufi, Arezki 5 Lacey, Michael T. 5 Li, Hongquan 5 Li, Xiang-Dong 5 Ly, Fu Ken 5 Orponen, Tuomas 5 Prisuelos-Arribas, Cruz 5 Rosén, Andreas 5 Seeger, Andreas 5 Sjogren, Peter 5 Tan, Chaoqiang 5 Vallarino, Maria 5 Volberg, Alexander Lvovich 5 Yang, Dongyong 5 Zhao, Zihui 4 Amenta, Alex 4 Bañuelos, Rodrigo 4 Brandolini, Luca 4 Castro, Alejandro J. 4 Cruz-Uribe, David Vincente 4 Deng, Qingquan 4 Engelstein, Max 4 Fackler, Stephan 4 Fariña, Juan Carlos 4 Geng, Jun 4 Georgiadis, Athanasios G. 4 Gigante, Giacomo ...and 602 more Authors all top 5 Cited in 177 Serials 52 Transactions of the American Mathematical Society 51 Journal of Functional Analysis 42 The Journal of Geometric Analysis 33 Journal of Mathematical Analysis and Applications 26 Potential Analysis 25 Advances in Mathematics 25 Revista Matemática Iberoamericana 24 Journal of Differential Equations 23 Mathematische Annalen 22 The Journal of Fourier Analysis and Applications 20 Mathematische Zeitschrift 20 Proceedings of the American Mathematical Society 14 Communications in Partial Differential Equations 13 Analysis & PDE 12 Journal de Mathématiques Pures et Appliquées. Neuvième Série 12 Science China. Mathematics 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 Acta Mathematica Sinica. English Series 10 Archive for Rational Mechanics and Analysis 10 Journal d’Analyse Mathématique 10 Calculus of Variations and Partial Differential Equations 9 Annales de l’Institut Fourier 9 Mathematische Nachrichten 9 SIAM Journal on Mathematical Analysis 9 Journal of Evolution Equations 9 Journal of the Australian Mathematical Society 8 Memoirs of the American Mathematical Society 8 Journal of Mathematical Sciences (New York) 7 Manuscripta Mathematica 7 Communications on Pure and Applied Analysis 7 Analysis in Theory and Applications 7 Journal of Function Spaces 6 Bulletin of the Australian Mathematical Society 6 Duke Mathematical Journal 6 Integral Equations and Operator Theory 6 Forum Mathematicum 6 Journal of the European Mathematical Society (JEMS) 6 Frontiers of Mathematics in China 6 Banach Journal of Mathematical Analysis 5 Inventiones Mathematicae 5 Journal of the Mathematical Society of Japan 5 Journal of the American Mathematical Society 5 Geometric and Functional Analysis. GAFA 5 Annales Academiae Scientiarum Fennicae. Mathematica 5 Revista Matemática Complutense 4 Communications on Pure and Applied Mathematics 4 Mathematical Methods in the Applied Sciences 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Czechoslovak Mathematical Journal 4 Illinois Journal of Mathematics 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Communications in Contemporary Mathematics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Bulletin of Mathematical Sciences 3 Communications in Mathematical Physics 3 Arkiv för Matematik 3 Acta Mathematica 3 Applied Mathematics and Optimization 3 Archiv der Mathematik 3 Journal of Approximation Theory 3 Journal für die Reine und Angewandte Mathematik 3 Mathematika 3 Probability Theory and Related Fields 3 Publicacions Matemàtiques 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Positivity 3 Taiwanese Journal of Mathematics 3 Journal of Mathematical Fluid Mechanics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Analysis and Geometry in Metric Spaces 2 Applicable Analysis 2 Inverse Problems 2 Israel Journal of Mathematics 2 Journal of Mathematical Physics 2 Mathematical Notes 2 Russian Mathematical Surveys 2 The Annals of Probability 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Collectanea Mathematica 2 Functional Analysis and its Applications 2 Indiana University Mathematics Journal 2 Journal of the Korean Mathematical Society 2 Nagoya Mathematical Journal 2 Numerische Mathematik 2 Proceedings of the London Mathematical Society. Third Series 2 Tohoku Mathematical Journal. Second Series 2 Constructive Approximation 2 Science in China. Series A 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Applied Mathematics. Series B (English Edition) 2 St. Petersburg Mathematical Journal 2 Georgian Mathematical Journal 2 Bulletin des Sciences Mathématiques 2 Journal of Inequalities and Applications 2 Mathematical Inequalities & Applications 2 Analysis and Applications (Singapore) 2 Boundary Value Problems 2 Complex Variables and Elliptic Equations ...and 77 more Serials all top 5 Cited in 46 Fields 475 Harmonic analysis on Euclidean spaces (42-XX) 423 Partial differential equations (35-XX) 197 Operator theory (47-XX) 135 Functional analysis (46-XX) 94 Global analysis, analysis on manifolds (58-XX) 88 Potential theory (31-XX) 55 Measure and integration (28-XX) 42 Probability theory and stochastic processes (60-XX) 30 Functions of a complex variable (30-XX) 30 Abstract harmonic analysis (43-XX) 25 Real functions (26-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 19 Fluid mechanics (76-XX) 18 Numerical analysis (65-XX) 16 Convex and discrete geometry (52-XX) 15 Number theory (11-XX) 13 Topological groups, Lie groups (22-XX) 12 Differential geometry (53-XX) 12 Mechanics of deformable solids (74-XX) 9 Integral equations (45-XX) 7 Ordinary differential equations (34-XX) 7 Quantum theory (81-XX) 5 Special functions (33-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Combinatorics (05-XX) 4 Integral transforms, operational calculus (44-XX) 4 General topology (54-XX) 4 Optics, electromagnetic theory (78-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Difference and functional equations (39-XX) 3 Approximations and expansions (41-XX) 3 Geometry (51-XX) 3 Statistics (62-XX) 3 Systems theory; control (93-XX) 3 Information and communication theory, circuits (94-XX) 2 Field theory and polynomials (12-XX) 2 Manifolds and cell complexes (57-XX) 2 Relativity and gravitational theory (83-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Group theory and generalizations (20-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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