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## Hofmann, Steve

Compute Distance To:
 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
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#### 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
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#### 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
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#### 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)

#### 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 1128.35316
Auscher, Pascal; Hofmann, Steve; Lacey, Michael; McIntosh, Alan; Tchamitchian, Ph.
2002
Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Zbl 1232.42018
Hofmann, Steve; Lu, Guozhen; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin
2011
Hardy and BMO spaces associated to divergence form elliptic operators. Zbl 1162.42012
Hofmann, Steve; Mayboroda, Svitlana
2009
Riesz transform on manifolds and heat kernel regularity. Zbl 1086.58013
Auscher, Pascal; Coulhon, Thierry; Duong, Xuan Thinh; Hofmann, Steve
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 1243.47072
Hofmann, Steve; Mayboroda, Svitlana; McIntosh, Alan
2011
$$L^p$$ bounds for Riesz transforms and square roots associated to second order elliptic operators. Zbl 1074.35031
Hofmann, Steve; Martell, José María
2003
Analyticity of layer potentials and $$L^{2}$$ solvability of boundary value problems for divergence form elliptic equations with complex $$L^{\infty }$$ coefficients. Zbl 1217.35056
Alfonseca, M. Angeles; Auscher, Pascal; Axelsson, Andreas; Hofmann, Steve; Kim, Seick
2011
The Green function estimates for strongly elliptic systems of second order. Zbl 1130.35042
Hofmann, Steve; Kim, Seick
2007
Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators. Zbl 1326.42028
Hofmann, Steve; Kenig, Carlos; Mayboroda, Svitlana; Pipher, Jill
2015
Singular integrals and elliptic boundary problems on regular Semmes-Kenig-Toro. Zbl 1221.31010
Hofmann, Steve; Mitrea, Marius; Taylor, Michael
2010
Carleson measures, trees, extrapolation, and $$T(b)$$ theorems. Zbl 1027.42009
Auscher, P.; Hofmann, S.; Muscalu, Camil; Tao, Terence C.; Thiele, Christoph
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 1302.31007
Hofmann, Steve; Martell, José María
2014
$$L^ 2$$ solvability and representation by caloric layer potentials in time-varying domains. Zbl 0867.35037
Hofmann, Steve; Lewis, John L.
1996
Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains. Zbl 1142.49021
Hofmann, Steve; Mitrea, Marius; Taylor, Michael
2007
The Kato square root problem for higher order elliptic operators and systems on $$\mathbb{R}^n$$. Zbl 1019.35029
Auscher, Pascal; Hofmann, Steve; McIntosh, Alan; Tchamitchian, Philippe
2001
Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems. Zbl 1157.35028
Auscher, Pascal; Axelsson, Andreas; Hofmann, Steve
2008
A new characterization of chord-arc domains. Zbl 1366.28004
Azzam, Jonas; Hofmann, Steve; Martell, José María; Nyström, Kaj; Toro, Tatiana
2017
Extrapolation of Carleson measures and the analyticity of Kato’s square-root operators. Zbl 1163.35346
Auscher, Pascal; Hofmann, Steve; Lewis, John L.; Tchamitchian, Philippe
2001
Rectifiability of harmonic measure. Zbl 1354.31004
Azzam, Jonas; Hofmann, Steve; Martell, José María; Mayboroda, Svitlana; Mourgoglou, Mihalis; Tolsa, Xavier; Volberg, Alexander
2016
The Dirichlet problem for parabolic operators with singular drift terms. Zbl 1149.35048
Hofmann, Steve; Lewis, John L.
2001
Uniform rectifiability and harmonic measure. II: Poisson kernels in $$L^p$$ imply uniform rectifiability. Zbl 1323.31008
Hofmann, Steve; Martell, José María; Uriarte-Tuero, Ignacio
2014
Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems. Zbl 1263.35080
Duong, Xuan Thinh; Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin
2013
The solution of the Kato problem for divergence from elliptic operators with Gaussian heat kernel bounds. Zbl 1128.35317
Hofmann, Steve; Lacey, Michael; McIntosh, Alan
2002
Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials. Zbl 0941.42006
Hofmann, Steve
1997
Weighted norm inequalities and vector valued inequalities for certain rough operators. Zbl 0804.42010
Hofmann, Steve
1993
The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients. Zbl 1325.42028
Hofmann, Steve; Kenig, Carlos; Mayboroda, Svitlana; Pipher, Jill
2015
Sharp rate of average decay of the Fourier transform of a bounded set. Zbl 1032.42017
Brandolini, L.; Hofmann, S.; Iosevich, A.
2003
Layer potentials and boundary value problems for elliptic equations with complex $$L^\infty$$ coefficients satisfying the small Carleson measure norm condition. Zbl 1311.35074
Hofmann, Steve; Mayboroda, Svitlana; Mourgoglou, Mihalis
2015
The method of layer potentials in $$L^{p}$$ and endpoint spaces for elliptic operators with $$L^{\infty}$$ coefficients. Zbl 1323.31011
Hofmann, Steve; Mitrea, Marius; Morris, Andrew J.
2015
Caloric measure in parabolic flat domains. Zbl 1074.35041
Hofmann, Steve; Lewis, John L.; Nyström, Kaj
2004
Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions. Zbl 1359.28005
Hofmann, Steve; Martell, José María; Mayboroda, Svitlana
2016
Vertical versus conical square functions. Zbl 1275.42028
Auscher, Pascal; Hofmann, Steve; Martell, José-María
2012
On certain nonstandard Calderón-Zygmund operators. Zbl 0826.42012
Hofmann, Steve
1994
The weak-$$A_\infty$$ property of harmonic and $$p$$-harmonic measures implies uniform rectifiability. Zbl 1369.31006
Hofmann, Steve; Le, Phi; Martell, José María; Nyström, Kaj
2017
Gaussian estimates for fundamental solutions to certain parabolic systems. Zbl 1061.35023
Hofmann, Steve; Kim, Seick
2004
The solution of the Kato problem in two dimensions. Zbl 1020.47031
Hofmann, Steve; McIntosh, Alan
2002
Circular averages and Falconer/Erdős distance conjecture in the plane for random metrics. Zbl 1096.28004
Hofmann, S.; Iosevich, A.
2005
Weak (1,1) boundedness of singular integrals with nonsmooth kernel. Zbl 0677.42013
Hofmann, Steve
1988
$$L^p$$-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets. Zbl 1371.28004
Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Morris, Andrew J.
2016
A local $$Tb$$ theorem for square functions. Zbl 1156.42307
Hofmann, Steve
2008
$$A_\infty$$ implies NTA for a class of variable coefficient elliptic operators. Zbl 1378.35092
Hofmann, Steve; Martell, José María; Toro, Tatiana
2017
Hardy spaces, singular integrals and the geometry of Euclidean domains of locally finite perimeter. Zbl 1333.42020
Hofmann, Steve; Marmolejo-Olea, Emilio; Mitrea, Marius; Pérez-Esteva, Salvador; Taylor, Michael
2009
Uniform rectifiability and harmonic measure. III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains. Zbl 1305.31005
Hofmann, Steve; Martell, José María; Mayboroda, Svitlana
2014
$$T1$$ theorems for Besov and Triebel-Lizorkin spaces. Zbl 0779.42010
Han, Y.-S.; Hofmann, Steve
1993
The $$L^p$$ Neumann problem for the heat equation in non-cylindrical domains. Zbl 1065.35125
Hofmann, Steve; Lewis, John L.
2005
Existence of big pieces of graphs for parabolic problems. Zbl 1046.35045
Hofmann, Steve; Lewis, John L.; Nyström, Kaj
2003
Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries. Zbl 1373.31003
Akman, Murat; Badger, Matthew; Hofmann, Steve; Martell, José María
2017
Boundedness and applications of singular integrals and square functions: a survey. Zbl 1255.42016
Hofmann, Steve; Mcintosh, Alan
2011
The solution of Kato’s conjectures. Zbl 1017.47034
Auscher, Pascal; Hofmann, Steve; Lacey, Michael; Lewis, John; McIntosh, Alan; Tchamitchian, Philippe
2001
On singular integrals of Calderón-type in $$\mathbb{R}^ n$$, and BMO. Zbl 0874.42011
Hofmann, Steve
1994
Square functions of Calderón type and applications. Zbl 0980.42011
Hofmann, Steve; Lewis, John L.
2001
Local $$Tb$$ theorems and applications in PDE. Zbl 1104.42007
Hofmann, Steve
2006
Symbol calculus for operators of layer potential type on Lipschitz surfaces with VMO normals, and related pseudodifferential operator calculus. Zbl 1317.31012
Hofmann, Steve; Mitrea, Marius; Taylor, Michael E.
2015
BMO solvability and absolute continuity of harmonic measure. Zbl 1405.42032
Hofmann, Steve; Le, Phi
2018
Dahlberg’s bilinear estimate for solutions of divergence form complex elliptic equations. Zbl 1172.42006
Hofmann, Steve
2008
A note on $$A_\infty$$ estimates via extrapolation of Carleson measures. Zbl 1228.42023
Hofmann, Steve; Martell, José María
2010
$$A_{\infty }$$ estimates via extrapolation of Carleson measures and applications to divergence form elliptic operators. Zbl 1247.42020
Hofmann, Steve; Martell, José María
2012
An off-diagonal $$T1$$ theorem and applications. Zbl 0919.42012
Hofmann, Steve
1998
A characterization of commutators of parabolic singular integrals. Zbl 1039.42500
Hofmann, Steve
1995
Boundedness criteria for rough singular integrals. Zbl 0831.42011
Hofmann, Steve
1995
Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains. Zbl 1036.35067
Hofmann, Steve; Lewis, John; Mitrea, Marius
2003
Square function estimates on layer potentials for higher-order elliptic equations. Zbl 1381.35035
Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana
2017
Rectifiability, interior approximation and harmonic measure. Zbl 1423.31002
Akman, Murat; Bortz, Simon; Hofmann, Steve; Martell, José María
2019
Local $$T(b)$$ theorems and applications in PDE. Zbl 1204.42023
Hofmann, Steve
2010
The $$L^p$$ regularity problem for the heat equation in non-cylindrical domains. Zbl 0934.35056
Hofmann, Steven; Lewis, John L.
1999
Generalized local $$Tb$$ theorems for square functions. Zbl 1366.42022
Grau de la Herrán, Ana; Hofmann, Steve
2017
Harmonic measure and approximation of uniformly rectifiable sets. Zbl 1371.28002
Bortz, Simon; Hofmann, Steve
2017
The Neumann problem for higher order elliptic equations with symmetric coefficients. Zbl 1394.35159
Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana
2018
Harmonic measure and quantitative connectivity: geometric characterization of the $$L^p$$-solvability of the Dirichlet problem. Zbl 1453.31009
Azzam, Jonas; Hofmann, Steve; Martell, José María; Mourgoglou, Mihalis; Tolsa, Xavier
2020
Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds. Zbl 1239.42013
Hofmann, Steve; Mitrea, Marius; Monniaux, Sylvie
2011
Dirichlet problems for a nonstationary linearized system of Navier-Stokes equations in non-cylindrical domains. Zbl 1057.35030
Hofmann, Steve; Nyström, Kaj
2002
Weighted weak-type (1,1) inequalities for rough operators. Zbl 0694.42024
Hofmann, Steve
1989
Singular integrals with power weights. Zbl 0717.42018
Hofmann, Steve
1990
A singular integral approach to a two phase free boundary problem. Zbl 1361.42012
Bortz, Simon; Hofmann, Steve
2016
A local $$Tb$$ theorem with vector-valued testing functions. Zbl 1345.42012
Grau de la Herrán, Ana; Hofmann, Steve
2016
Perturbations of elliptic operators in 1-sided chord-arc domains. II: Non-symmetric operators and Carleson measure estimates. Zbl 1453.31011
Cavero, Juan; Hofmann, Steve; Martell, José María; Toro, Tatiana
2020
Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress. Zbl 1421.31010
Hofmann, Steve
2019
The commutator of the Kato square root for second order elliptic operators on $$\mathbb{R}^n$$. Zbl 1351.42027
Chen, Yan Ping; Ding, Yong; Hofmann, Steve
2016
On stability of square root domains for non-self-adjoint operators under additive perturbations. Zbl 1345.47015
Gesztesy, Fritz; Hofmann, Steve; Nichols, Roger
2016
Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains. Zbl 1308.35082
Gesztesy, Fritz; Hofmann, Steve; Nichols, Roger
2015
The Calderón commutator along a parabola. Zbl 0948.42009
Carbery, Anthony; Hofmann, Steve; Wright, James
1999
A short course on the Kato problem. Zbl 1012.47013
Hofmann, Steve
2001
Lattice points inside random ellipsoids. Zbl 1056.11052
Hofmann, S.; Iosevich, A.; Weidinger, D.
2004
Perturbations of elliptic operators in 1-sided chord-arc domains. I: Small and large perturbation for symmetric operators. Zbl 1410.31003
Cavero, Juan; Hofmann, Steve; Martell, José María
2019
A weak reverse Hölder inequality for caloric measure. Zbl 1436.42028
Genschaw, Alyssa; Hofmann, Steve
2020
Uniform rectifiability and $$\varepsilon$$-approximability of harmonic functions in $$L^p$$. (Rectifiabilité uniforme et $$\varepsilon$$-approximation dans $$L^p$$.) Zbl 1465.42024
Hofmann, Steve; Tapiola, Olli
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 1432.35091
Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana
2019
A generalized characterization of commutators of parabolic singular integrals. Zbl 0953.42008
Hofmann, Steve; Li, Xinwei; Yang, Dachun
1999
A weak molecule condition for certain Triebel-Lizorkin spaces. Zbl 0811.46025
Hofmann, Steve
1992
Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets. Zbl 1286.28003
Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Morris, Andrew J.
2014
Kato square root problem with unbounded leading coefficients. Zbl 1400.35041
Escauriaza, Luis; Hofmann, Steve
2018
Quantitative Fatou theorems and uniform rectifiability. Zbl 1453.31010
Bortz, Simon; Hofmann, Steve
2020
Harmonic measure and quantitative connectivity: geometric characterization of the $$L^p$$-solvability of the Dirichlet problem. Zbl 1453.31009
Azzam, Jonas; Hofmann, Steve; Martell, José María; Mourgoglou, Mihalis; Tolsa, Xavier
2020
Perturbations of elliptic operators in 1-sided chord-arc domains. II: Non-symmetric operators and Carleson measure estimates. Zbl 1453.31011
Cavero, Juan; Hofmann, Steve; Martell, José María; Toro, Tatiana
2020
A weak reverse Hölder inequality for caloric measure. Zbl 1436.42028
Genschaw, Alyssa; Hofmann, Steve
2020
Uniform rectifiability and $$\varepsilon$$-approximability of harmonic functions in $$L^p$$. (Rectifiabilité uniforme et $$\varepsilon$$-approximation dans $$L^p$$.) Zbl 1465.42024
Hofmann, Steve; Tapiola, Olli
2020
Quantitative Fatou theorems and uniform rectifiability. Zbl 1453.31010
Bortz, Simon; Hofmann, Steve
2020
Rectifiability, interior approximation and harmonic measure. Zbl 1423.31002
Akman, Murat; Bortz, Simon; Hofmann, Steve; Martell, José María
2019
Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress. Zbl 1421.31010
Hofmann, Steve
2019
Perturbations of elliptic operators in 1-sided chord-arc domains. I: Small and large perturbation for symmetric operators. Zbl 1410.31003
Cavero, Juan; Hofmann, Steve; Martell, José María
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 1432.35091
Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana
2019
BMO solvability and absolute continuity of harmonic measure. Zbl 1405.42032
Hofmann, Steve; Le, Phi
2018
The Neumann problem for higher order elliptic equations with symmetric coefficients. Zbl 1394.35159
Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana
2018
Kato square root problem with unbounded leading coefficients. Zbl 1400.35041
Escauriaza, Luis; Hofmann, Steve
2018
A new characterization of chord-arc domains. Zbl 1366.28004
Azzam, Jonas; Hofmann, Steve; Martell, José María; Nyström, Kaj; Toro, Tatiana
2017
The weak-$$A_\infty$$ property of harmonic and $$p$$-harmonic measures implies uniform rectifiability. Zbl 1369.31006
Hofmann, Steve; Le, Phi; Martell, José María; Nyström, Kaj
2017
$$A_\infty$$ implies NTA for a class of variable coefficient elliptic operators. Zbl 1378.35092
Hofmann, Steve; Martell, José María; Toro, Tatiana
2017
Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries. Zbl 1373.31003
Akman, Murat; Badger, Matthew; Hofmann, Steve; Martell, José María
2017
Square function estimates on layer potentials for higher-order elliptic equations. Zbl 1381.35035
Barton, Ariel; Hofmann, Steve; Mayboroda, Svitlana
2017
Generalized local $$Tb$$ theorems for square functions. Zbl 1366.42022
Grau de la Herrán, Ana; Hofmann, Steve
2017
Harmonic measure and approximation of uniformly rectifiable sets. Zbl 1371.28002
Bortz, Simon; Hofmann, Steve
2017
Rectifiability of harmonic measure. Zbl 1354.31004
Azzam, Jonas; Hofmann, Steve; Martell, José María; Mayboroda, Svitlana; Mourgoglou, Mihalis; Tolsa, Xavier; Volberg, Alexander
2016
Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions. Zbl 1359.28005
Hofmann, Steve; Martell, José María; Mayboroda, Svitlana
2016
$$L^p$$-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets. Zbl 1371.28004
Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Morris, Andrew J.
2016
A singular integral approach to a two phase free boundary problem. Zbl 1361.42012
Bortz, Simon; Hofmann, Steve
2016
A local $$Tb$$ theorem with vector-valued testing functions. Zbl 1345.42012
Grau de la Herrán, Ana; Hofmann, Steve
2016
The commutator of the Kato square root for second order elliptic operators on $$\mathbb{R}^n$$. Zbl 1351.42027
Chen, Yan Ping; Ding, Yong; Hofmann, Steve
2016
On stability of square root domains for non-self-adjoint operators under additive perturbations. Zbl 1345.47015
Gesztesy, Fritz; Hofmann, Steve; Nichols, Roger
2016
Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators. Zbl 1326.42028
Hofmann, Steve; Kenig, Carlos; Mayboroda, Svitlana; Pipher, Jill
2015
The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients. Zbl 1325.42028
Hofmann, Steve; Kenig, Carlos; Mayboroda, Svitlana; Pipher, Jill
2015
Layer potentials and boundary value problems for elliptic equations with complex $$L^\infty$$ coefficients satisfying the small Carleson measure norm condition. Zbl 1311.35074
Hofmann, Steve; Mayboroda, Svitlana; Mourgoglou, Mihalis
2015
The method of layer potentials in $$L^{p}$$ and endpoint spaces for elliptic operators with $$L^{\infty}$$ coefficients. Zbl 1323.31011
Hofmann, Steve; Mitrea, Marius; Morris, Andrew J.
2015
Symbol calculus for operators of layer potential type on Lipschitz surfaces with VMO normals, and related pseudodifferential operator calculus. Zbl 1317.31012
Hofmann, Steve; Mitrea, Marius; Taylor, Michael E.
2015
Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains. Zbl 1308.35082
Gesztesy, Fritz; Hofmann, Steve; Nichols, Roger
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 1302.31007
Hofmann, Steve; Martell, José María
2014
Uniform rectifiability and harmonic measure. II: Poisson kernels in $$L^p$$ imply uniform rectifiability. Zbl 1323.31008
Hofmann, Steve; Martell, José María; Uriarte-Tuero, Ignacio
2014
Uniform rectifiability and harmonic measure. III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains. Zbl 1305.31005
Hofmann, Steve; Martell, José María; Mayboroda, Svitlana
2014
Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets. Zbl 1286.28003
Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Morris, Andrew J.
2014
Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems. Zbl 1263.35080
Duong, Xuan Thinh; Hofmann, Steve; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin
2013
Vertical versus conical square functions. Zbl 1275.42028
Auscher, Pascal; Hofmann, Steve; Martell, José-María
2012
$$A_{\infty }$$ estimates via extrapolation of Carleson measures and applications to divergence form elliptic operators. Zbl 1247.42020
Hofmann, Steve; Martell, José María
2012
Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Zbl 1232.42018
Hofmann, Steve; Lu, Guozhen; Mitrea, Dorina; Mitrea, Marius; Yan, Lixin
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 1243.47072
Hofmann, Steve; Mayboroda, Svitlana; McIntosh, Alan
2011
Analyticity of layer potentials and $$L^{2}$$ solvability of boundary value problems for divergence form elliptic equations with complex $$L^{\infty }$$ coefficients. Zbl 1217.35056
Alfonseca, M. Angeles; Auscher, Pascal; Axelsson, Andreas; Hofmann, Steve; Kim, Seick
2011
Boundedness and applications of singular integrals and square functions: a survey. Zbl 1255.42016
Hofmann, Steve; Mcintosh, Alan
2011
Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds. Zbl 1239.42013
Hofmann, Steve; Mitrea, Marius; Monniaux, Sylvie
2011
Singular integrals and elliptic boundary problems on regular Semmes-Kenig-Toro. Zbl 1221.31010
Hofmann, Steve; Mitrea, Marius; Taylor, Michael
2010
A note on $$A_\infty$$ estimates via extrapolation of Carleson measures. Zbl 1228.42023
Hofmann, Steve; Martell, José María
2010
Local $$T(b)$$ theorems and applications in PDE. Zbl 1204.42023
Hofmann, Steve
2010
Hardy and BMO spaces associated to divergence form elliptic operators. Zbl 1162.42012
Hofmann, Steve; Mayboroda, Svitlana
2009
Hardy spaces, singular integrals and the geometry of Euclidean domains of locally finite perimeter. Zbl 1333.42020
Hofmann, Steve; Marmolejo-Olea, Emilio; Mitrea, Marius; Pérez-Esteva, Salvador; Taylor, Michael
2009
Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems. Zbl 1157.35028
Auscher, Pascal; Axelsson, Andreas; Hofmann, Steve
2008
A local $$Tb$$ theorem for square functions. Zbl 1156.42307
Hofmann, Steve
2008
Dahlberg’s bilinear estimate for solutions of divergence form complex elliptic equations. Zbl 1172.42006
Hofmann, Steve
2008
The Green function estimates for strongly elliptic systems of second order. Zbl 1130.35042
Hofmann, Steve; Kim, Seick
2007
Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains. Zbl 1142.49021
Hofmann, Steve; Mitrea, Marius; Taylor, Michael
2007
Local $$Tb$$ theorems and applications in PDE. Zbl 1104.42007
Hofmann, Steve
2006
Circular averages and Falconer/Erdős distance conjecture in the plane for random metrics. Zbl 1096.28004
Hofmann, S.; Iosevich, A.
2005
The $$L^p$$ Neumann problem for the heat equation in non-cylindrical domains. Zbl 1065.35125
Hofmann, Steve; Lewis, John L.
2005
Riesz transform on manifolds and heat kernel regularity. Zbl 1086.58013
Auscher, Pascal; Coulhon, Thierry; Duong, Xuan Thinh; Hofmann, Steve
2004
Caloric measure in parabolic flat domains. Zbl 1074.35041
Hofmann, Steve; Lewis, John L.; Nyström, Kaj
2004
Gaussian estimates for fundamental solutions to certain parabolic systems. Zbl 1061.35023
Hofmann, Steve; Kim, Seick
2004
Lattice points inside random ellipsoids. Zbl 1056.11052
Hofmann, S.; Iosevich, A.; Weidinger, D.
2004
$$L^p$$ bounds for Riesz transforms and square roots associated to second order elliptic operators. Zbl 1074.35031
Hofmann, Steve; Martell, José María
2003
Sharp rate of average decay of the Fourier transform of a bounded set. Zbl 1032.42017
Brandolini, L.; Hofmann, S.; Iosevich, A.
2003
Existence of big pieces of graphs for parabolic problems. Zbl 1046.35045
Hofmann, Steve; Lewis, John L.; Nyström, Kaj
2003
Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains. Zbl 1036.35067
Hofmann, Steve; Lewis, John; Mitrea, Marius
2003
The solution of the Kato square root problem for second order elliptic operators on $$\mathbb R^n$$. Zbl 1128.35316
Auscher, Pascal; Hofmann, Steve; Lacey, Michael; McIntosh, Alan; Tchamitchian, Ph.
2002
Carleson measures, trees, extrapolation, and $$T(b)$$ theorems. Zbl 1027.42009
Auscher, P.; Hofmann, S.; Muscalu, Camil; Tao, Terence C.; Thiele, Christoph
2002
The solution of the Kato problem for divergence from elliptic operators with Gaussian heat kernel bounds. Zbl 1128.35317
Hofmann, Steve; Lacey, Michael; McIntosh, Alan
2002
The solution of the Kato problem in two dimensions. Zbl 1020.47031
Hofmann, Steve; McIntosh, Alan
2002
Dirichlet problems for a nonstationary linearized system of Navier-Stokes equations in non-cylindrical domains. Zbl 1057.35030
Hofmann, Steve; Nyström, Kaj
2002
The Kato square root problem for higher order elliptic operators and systems on $$\mathbb{R}^n$$. Zbl 1019.35029
Auscher, Pascal; Hofmann, Steve; McIntosh, Alan; Tchamitchian, Philippe
2001
Extrapolation of Carleson measures and the analyticity of Kato’s square-root operators. Zbl 1163.35346
Auscher, Pascal; Hofmann, Steve; Lewis, John L.; Tchamitchian, Philippe
2001
The Dirichlet problem for parabolic operators with singular drift terms. Zbl 1149.35048
Hofmann, Steve; Lewis, John L.
2001
The solution of Kato’s conjectures. Zbl 1017.47034
Auscher, Pascal; Hofmann, Steve; Lacey, Michael; Lewis, John; McIntosh, Alan; Tchamitchian, Philippe
2001
Square functions of Calderón type and applications. Zbl 0980.42011
Hofmann, Steve; Lewis, John L.
2001
A short course on the Kato problem. Zbl 1012.47013
Hofmann, Steve
2001
The $$L^p$$ regularity problem for the heat equation in non-cylindrical domains. Zbl 0934.35056
Hofmann, Steven; Lewis, John L.
1999
The Calderón commutator along a parabola. Zbl 0948.42009
Carbery, Anthony; Hofmann, Steve; Wright, James
1999
A generalized characterization of commutators of parabolic singular integrals. Zbl 0953.42008
Hofmann, Steve; Li, Xinwei; Yang, Dachun
1999
An off-diagonal $$T1$$ theorem and applications. Zbl 0919.42012
Hofmann, Steve
1998
Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials. Zbl 0941.42006
Hofmann, Steve
1997
$$L^ 2$$ solvability and representation by caloric layer potentials in time-varying domains. Zbl 0867.35037
Hofmann, Steve; Lewis, John L.
1996
A characterization of commutators of parabolic singular integrals. Zbl 1039.42500
Hofmann, Steve
1995
Boundedness criteria for rough singular integrals. Zbl 0831.42011
Hofmann, Steve
1995
On certain nonstandard Calderón-Zygmund operators. Zbl 0826.42012
Hofmann, Steve
1994
On singular integrals of Calderón-type in $$\mathbb{R}^ n$$, and BMO. Zbl 0874.42011
Hofmann, Steve
1994
Weighted norm inequalities and vector valued inequalities for certain rough operators. Zbl 0804.42010
Hofmann, Steve
1993
$$T1$$ theorems for Besov and Triebel-Lizorkin spaces. Zbl 0779.42010
Han, Y.-S.; Hofmann, Steve
1993
A weak molecule condition for certain Triebel-Lizorkin spaces. Zbl 0811.46025
Hofmann, Steve
1992
Singular integrals with power weights. Zbl 0717.42018
Hofmann, Steve
1990
Weighted weak-type (1,1) inequalities for rough operators. Zbl 0694.42024
Hofmann, Steve
1989
Weak (1,1) boundedness of singular integrals with nonsmooth kernel. Zbl 0677.42013
Hofmann, Steve
1988
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)

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