Kim, Elena; Ogden, W. Jacob; Reerink, Tommie; Zeytuncu, Yunus E. Sobolev and Schatten estimates for the complex Green operator on spheres. (English) Zbl 1436.32118 New York J. Math. 26, 261-271 (2020). MSC: 32W05 47B10 PDF BibTeX XML Cite \textit{E. Kim} et al., New York J. Math. 26, 261--271 (2020; Zbl 1436.32118) Full Text: Link
Bei, Francesco On the Laplace-Beltrami operator on compact complex spaces. (English) Zbl 07130347 Trans. Am. Math. Soc. 372, No. 12, 8477-8505 (2019). Reviewer: Petar Popivanov (Sofia) MSC: 32W05 32W50 PDF BibTeX XML Cite \textit{F. Bei}, Trans. Am. Math. Soc. 372, No. 12, 8477--8505 (2019; Zbl 07130347) Full Text: DOI arXiv
Bei, Francesco Degenerating Hermitian metrics and spectral geometry of the canonical bundle. (English) Zbl 1408.32009 Adv. Math. 328, 750-800 (2018). Reviewer: Daniel Barlet (Vandœuvre-les-Nancy) MSC: 32C15 32W05 32W50 35P15 58J35 PDF BibTeX XML Cite \textit{F. Bei}, Adv. Math. 328, 750--800 (2018; Zbl 1408.32009) Full Text: DOI arXiv
Haslinger, Friedrich Complex analysis. A functional analytic approach. (English) Zbl 1393.30001 De Gruyter Graduate. Berlin: De Gruyter (ISBN 978-3-11-041723-4/pbk; 978-3-11-041724-1/ebook). ix, 338 p. (2018). Reviewer: Raymond Mortini (Metz) MSC: 30-01 32-01 30H20 32A10 32W05 47-01 47B38 47F05 35N15 PDF BibTeX XML Cite \textit{F. Haslinger}, Complex analysis. A functional analytic approach. Berlin: De Gruyter (2018; Zbl 1393.30001) Full Text: DOI
Casarino, Valentina; Cowling, Michael G.; Martini, Alessio; Sikora, Adam Spectral multipliers for the Kohn Laplacian on forms on the sphere in \(\mathbb {C}^n\). (English) Zbl 1392.32017 J. Geom. Anal. 27, No. 4, 3302-3338 (2017). MSC: 32V40 32V20 32W05 PDF BibTeX XML Cite \textit{V. Casarino} et al., J. Geom. Anal. 27, No. 4, 3302--3338 (2017; Zbl 1392.32017) Full Text: DOI
Fu, Siqi; Laurent-Thiébaut, Christine; Shaw, Mei-Chi Hearing pseudoconvexity in Lipschitz domains with holes via \({\bar{\partial }}\). (English) Zbl 1390.32007 Math. Z. 287, No. 3-4, 1157-1181 (2017). Reviewer: Harold P. Boas (College Station) MSC: 32C35 32C37 32W05 PDF BibTeX XML Cite \textit{S. Fu} et al., Math. Z. 287, No. 3--4, 1157--1181 (2017; Zbl 1390.32007) Full Text: DOI
Keller, Julien; Meyer, Julien; Seyyedali, Reza Quantization of the Laplacian operator on vector bundles. I. (English) Zbl 1353.53093 Math. Ann. 366, No. 3-4, 865-907 (2016). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 53D50 47F05 35P20 53D20 32W05 14L24 PDF BibTeX XML Cite \textit{J. Keller} et al., Math. Ann. 366, No. 3--4, 865--907 (2016; Zbl 1353.53093) Full Text: DOI arXiv
Berger, Franz Essential spectra of tensor product Hilbert complexes and the \(\overline{\partial}\)-Neumann problem on product manifolds. (English) Zbl 1350.58009 J. Funct. Anal. 271, No. 6, 1434-1461 (2016). Reviewer: Vamsi Pritham Pingali (Baltimore) MSC: 58J10 58J50 35N15 47A13 PDF BibTeX XML Cite \textit{F. Berger}, J. Funct. Anal. 271, No. 6, 1434--1461 (2016; Zbl 1350.58009) Full Text: DOI arXiv
Dubey, Shivani; Kumar, Ajay; Mishra, Mukund Madhav The Neumann problem for the Kohn-Laplacian on the Heisenberg group \(\mathbb H_n\). (English) Zbl 1345.31010 Potential Anal. 45, No. 1, 119-133 (2016). Reviewer: Paolo Musolino (Padova) MSC: 31B20 35N15 33C55 45B05 PDF BibTeX XML Cite \textit{S. Dubey} et al., Potential Anal. 45, No. 1, 119--133 (2016; Zbl 1345.31010) Full Text: DOI
Tran Vu Khanh Equivalence of estimates on a domain and its boundary. (English) Zbl 1336.32030 Vietnam J. Math. 44, No. 1, 29-48 (2016). MSC: 32T99 32W05 PDF BibTeX XML Cite \textit{Tran Vu Khanh}, Vietnam J. Math. 44, No. 1, 29--48 (2016; Zbl 1336.32030) Full Text: DOI
Dall’Ara, Gian Maria Pointwise estimates of weighted Bergman kernels in several complex variables. (English) Zbl 1329.32022 Adv. Math. 285, 1706-1740 (2015). Reviewer: Fritz Haslinger (Wien) MSC: 32W05 32W30 32A36 47F05 PDF BibTeX XML Cite \textit{G. M. Dall'Ara}, Adv. Math. 285, 1706--1740 (2015; Zbl 1329.32022) Full Text: DOI arXiv
Haslinger, Friedrich The \(\bar \partial\) Neumann problem and Schrödinger operators. (English) Zbl 1316.32001 De Gruyter Expositions in Mathematics 59. Berlin: De Gruyter (ISBN 978-3-11-031530-1/hbk; 978-3-11-031535-6/ebook). xi, 241 p. (2014). Reviewer: Harold P. Boas (College Station) MSC: 32-02 32A25 32A36 32W05 35J10 PDF BibTeX XML Cite \textit{F. Haslinger}, The \(\bar \partial\) Neumann problem and Schrödinger operators. Berlin: De Gruyter (2014; Zbl 1316.32001)
Khanh, Tran Vu; Pinton, Stefano; Zampieri, Giuseppe Compactness estimates for \(\square_{b}\) on a CR manifold. (English) Zbl 1300.32036 Proc. Am. Math. Soc. 140, No. 9, 3229-3236 (2012). Reviewer: Mauro Nacinovich (Roma) MSC: 32W05 32W10 32T25 PDF BibTeX XML Cite \textit{T. V. Khanh} et al., Proc. Am. Math. Soc. 140, No. 9, 3229--3236 (2012; Zbl 1300.32036) Full Text: DOI arXiv
Fu, Siqi; Jacobowitz, Howard The \(\overline\partial\)-cohomology groups, holomorphic Morse inequalities, and finite type conditions. (English) Zbl 1214.32016 Pure Appl. Math. Q. 6, No. 3, 875-914 (2010). Reviewer: Jean Ruppenthal (Wuppertal) MSC: 32W05 32L10 PDF BibTeX XML Cite \textit{S. Fu} and \textit{H. Jacobowitz}, Pure Appl. Math. Q. 6, No. 3, 875--914 (2010; Zbl 1214.32016) Full Text: DOI arXiv
Chakrabarti, Debraj Spectrum of the complex Laplacian on product domains. (English) Zbl 1225.32039 Proc. Am. Math. Soc. 138, No. 9, 3187-3202 (2010). Reviewer: Manuel Flores (La Laguna) MSC: 32W05 35N15 PDF BibTeX XML Cite \textit{D. Chakrabarti}, Proc. Am. Math. Soc. 138, No. 9, 3187--3202 (2010; Zbl 1225.32039) Full Text: DOI arXiv
Chang, Der-Chen; Yau, Stephen S.-T. Geometric analysis on a family of pseudoconvex hypersurfaces. (English) Zbl 1227.35011 Lee, Yng-Ing (ed.) et al., Recent advances in geometric analysis. Proceeding of the international conference on geometric analysis, Taipei, Taiwan, June 18–22, 2007. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-143-8/pbk). Advanced Lectures in Mathematics (ALM) 11, 61-99 (2010). MSC: 35A08 35A20 35H20 53C22 53C17 32W05 PDF BibTeX XML Cite \textit{D.-C. Chang} and \textit{S. S. T. Yau}, in: Recent advances in geometric analysis. Proceeding of the international conference on geometric analysis, Taipei, Taiwan, June 18--22, 2007. Somerville, MA: International Press; Beijing: Higher Education Press. 61--99 (2010; Zbl 1227.35011)
Fu, Siqi Positivity of the \(\overline\partial\)-Neumann Laplacian. (English) Zbl 1209.32022 Ebenfelt, Peter (ed.) et al., Complex analysis. Several complex variables and connections with PDE theory and geometry. Proceedings of the conference in honour of Linda Rothschild, Fribourg, Switzerland, July 7–11, 2008. Basel: Birkhäuser (ISBN 978-3-0346-0008-8/hbk). Trends in Mathematics, 145-158 (2010). Reviewer: Hong Rae Cho (Busan) MSC: 32W05 32Q28 PDF BibTeX XML Cite \textit{S. Fu}, in: Complex analysis. Several complex variables and connections with PDE theory and geometry. Proceedings of the conference in honour of Linda Rothschild, Fribourg, Switzerland, July 7--11, 2008. Basel: Birkhäuser. 145--158 (2010; Zbl 1209.32022) Full Text: arXiv
Shaw, Mei-Chi; Wang, Lihe Maximal \(L^2\) and pointwise Hölder estimates for \(\square_b\) on \(CR\) manifolds of class \(C^2\). (English) Zbl 1156.32024 Commun. Partial Differ. Equations 33, No. 9, 1690-1710 (2008). Reviewer: Gheorghe Gussi (Bucureşti) MSC: 32W10 32W05 35N15 PDF BibTeX XML Cite \textit{M.-C. Shaw} and \textit{L. Wang}, Commun. Partial Differ. Equations 33, No. 9, 1690--1710 (2008; Zbl 1156.32024) Full Text: DOI
Fu, Siqi Hearing the type of a domain in \(\mathbb C^2\) with the \(\bar{\partial}\)-Neumann Laplacian. (English) Zbl 1156.32023 Adv. Math. 219, No. 2, 568-603 (2008). Reviewer: Gheorghe Gussi (Bucureşti) MSC: 32W05 32N15 PDF BibTeX XML Cite \textit{S. Fu}, Adv. Math. 219, No. 2, 568--603 (2008; Zbl 1156.32023) Full Text: DOI arXiv
Koenig, Kenneth D. Comparing the Bergman and Szegö projections on domains with subelliptic boundary Laplacian. (English) Zbl 1180.32014 Math. Ann. 339, No. 3, 667-693 (2007). Reviewer: Lou Zengjian (Shantou Guangdong) MSC: 32W05 32W10 PDF BibTeX XML Cite \textit{K. D. Koenig}, Math. Ann. 339, No. 3, 667--693 (2007; Zbl 1180.32014) Full Text: DOI
Fu, Siqi Spectrum of the \(\overline{\partial}\)-Neumann Laplacian on polydiscs. (English) Zbl 1118.32026 Proc. Am. Math. Soc. 135, No. 3, 725-730 (2007). Reviewer: Joachim Michel (Calais) MSC: 32W05 33C10 PDF BibTeX XML Cite \textit{S. Fu}, Proc. Am. Math. Soc. 135, No. 3, 725--730 (2007; Zbl 1118.32026) Full Text: DOI arXiv
Hörmander, Lars The null space of the \(\overline \partial \)-Neumann operator. (English) Zbl 1083.32033 Ann. Inst. Fourier 54, No. 5, 1305-1369 (2004). Reviewer: Emil J. Straube (College Station) MSC: 32W05 32A25 PDF BibTeX XML Cite \textit{L. Hörmander}, Ann. Inst. Fourier 54, No. 5, 1305--1369 (2004; Zbl 1083.32033) Full Text: DOI Numdam EuDML
Peloso, Marco M.; Ricci, Fulvio Analysis of the Kohn Laplacian on quadratic CR manifolds. (English) Zbl 1043.32021 J. Funct. Anal. 203, No. 2, 321-355 (2003). Reviewer: Gheorghe Gussi (Bucureşti) MSC: 32V20 32W10 35N15 PDF BibTeX XML Cite \textit{M. M. Peloso} and \textit{F. Ricci}, J. Funct. Anal. 203, No. 2, 321--355 (2003; Zbl 1043.32021) Full Text: DOI
Ehsani, Dariush Solution of the \(\bar{\partial}\)-Neumann problem on a non-smooth domain. (English) Zbl 1056.32024 Indiana Univ. Math. J. 52, No. 3, 629-666 (2003). Reviewer: Der-Chen Chang (Washington D. C.) MSC: 32W05 35B65 PDF BibTeX XML Cite \textit{D. Ehsani}, Indiana Univ. Math. J. 52, No. 3, 629--666 (2003; Zbl 1056.32024) Full Text: DOI arXiv
Christ, Michael Hypoellipticity of the Kohn Laplacian for three-dimensional tubular Cauchy-Riemann structures. (English) Zbl 1038.32031 J. Inst. Math. Jussieu 1, No. 2, 279-291 (2002). Reviewer: Jih-Hsin Cheng (Taipei) MSC: 32V20 32V15 32T27 32W05 35H10 35J70 PDF BibTeX XML Cite \textit{M. Christ}, J. Inst. Math. Jussieu 1, No. 2, 279--291 (2002; Zbl 1038.32031) Full Text: DOI
Ueki, N. Estimates on the heat kernel of the Pauli Hamiltonian and its application to problems on hypoellipticity of the \(\overline\partial_b\)-Laplacian. (English) Zbl 1038.32035 Math. Z. 239, No. 1, 69-97 (2002). Reviewer: Lee Taichung (Hsinchu) MSC: 32W30 32W10 35N15 PDF BibTeX XML Cite \textit{N. Ueki}, Math. Z. 239, No. 1, 69--97 (2002; Zbl 1038.32035) Full Text: DOI
Lieb, Ingo; Michel, Joachim The Cauchy-Riemann complex. Integral formulae and Neumann problem. (English) Zbl 0994.32002 Aspects of Mathematics. E 34. Wiesbaden: Vieweg. x, 362 p. (2002). Reviewer: Eleonora Storozhenko (Odessa) MSC: 32A25 32-02 32W05 35N15 32E40 35-02 32A26 32C55 32E10 PDF BibTeX XML Cite \textit{I. Lieb} and \textit{J. Michel}, The Cauchy-Riemann complex. Integral formulae and Neumann problem. Wiesbaden: Vieweg (2002; Zbl 0994.32002)
Wang, Wei Regularity of \(\overline\partial_b\) complex on nondegenerate Cauchy-Riemann manifolds. (English) Zbl 1005.32025 Sci. China, Ser. A 44, No. 4, 452-466 (2001). MSC: 32W10 32V20 35A17 35N15 PDF BibTeX XML Cite \textit{W. Wang}, Sci. China, Ser. A 44, No. 4, 452--466 (2001; Zbl 1005.32025) Full Text: DOI
Berenstein, Carlos; Chang, Der-Chen; Tie, Jingzhi Laguerre calculus and its applications on the Heisenberg group. (English) Zbl 0986.22008 AMS/IP Studies in Advanced Mathematics. 22. Providence, RI: American Mathematical Society (AMS). xii, 319 p. (2001). Reviewer: K.Saka (Akita) MSC: 22E30 43A80 22-02 43-02 33C20 42C10 47G30 32W05 32A10 30E99 PDF BibTeX XML Cite \textit{C. Berenstein} et al., Laguerre calculus and its applications on the Heisenberg group. Providence, RI: American Mathematical Society (AMS) (2001; Zbl 0986.22008)
Iwasaki, Chisato A new construction of an asymptotics for the fundamental solutions for parabolic initial-boundary problem and its application to the \(\bar\partial\)-Neumann problem. (English) Zbl 0927.58012 Noguchi, J. (ed.) et al., Geometric complex analysis. Proceedings of the conference held at the 3rd International Research Institute of the Mathematical Society of Japan, Hayama, March 19–29, 1995. Singapore: World Scientific. 287-295 (1996). MSC: 58J32 58J35 32W05 PDF BibTeX XML Cite \textit{C. Iwasaki}, in: Geometric complex analysis. Proceedings of the conference held at the 3rd International Research Institute of the Mathematical Society of Japan, Hayama, March 19--29, 1995. Singapore: World Scientific. 287--295 (1996; Zbl 0927.58012)
Derridj, Makhlouf Hölder regularity for \(\square_ b\) on hypersurfaces in \(\mathbb{C}^ n\) with nondiagonalizable Levi form. (English) Zbl 0856.32010 Ancona, Vincenzo (ed.) et al., Complex analysis and geometry. Proceedings of the conference held in Trento, Italy, June 5-9, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 173, 135-154 (1996). Reviewer: A.Tancredi (Perugia) MSC: 32W05 32T99 32V99 PDF BibTeX XML Cite \textit{M. Derridj}, Lect. Notes Pure Appl. Math. 173, 135--154 (1996; Zbl 0856.32010)
Zhang, Jinhao Beltrami equation in high dimensions. (English) Zbl 0799.32017 Yang, Chung-Chun (ed.) et al., Several complex variables in China. Providence, RI: American Mathematical Society. Contemp. Math. 142, 143-150 (1993). Reviewer: A.Džuraev (Berlin) MSC: 32G05 32-02 30C65 32W05 35N05 PDF BibTeX XML Cite \textit{J. Zhang}, Contemp. Math. 142, 143--150 (1993; Zbl 0799.32017)
Grigis, Alain; Rothschild, Linda Preiss \(L^ 2\) estimates for the boundary Laplacian operator on hypersurfaces. (English) Zbl 0675.35064 Am. J. Math. 110, No. 4, 577-593 (1988). Reviewer: M.Merigot MSC: 35N15 35J05 35B45 PDF BibTeX XML Cite \textit{A. Grigis} and \textit{L. P. Rothschild}, Am. J. Math. 110, No. 4, 577--593 (1988; Zbl 0675.35064) Full Text: DOI
Derridj, Makhlouf; Tartakoff, David S. Local analyticity for \(\square{}_ b\) and the \(\bar\partial\)-Neumann problem at certain weakly pseudoconvex points. (English) Zbl 0736.35070 Commun. Partial Differ. Equations 13, No. 12, 1521-1600 (1988). Reviewer: H.P.Boas (College Station) MSC: 35N15 32W05 PDF BibTeX XML Cite \textit{M. Derridj} and \textit{D. S. Tartakoff}, Commun. Partial Differ. Equations 13, No. 12, 1521--1600 (1988; Zbl 0736.35070) Full Text: DOI
Beals, Richard; Stanton, Nancy K. The heat equation for the \({\bar\partial}\)-Neumann problem. I. (English) Zbl 0615.58033 Commun. Partial Differ. Equations 12, 351-413 (1987). Reviewer: C.Zuily MSC: 58J35 35K05 35N15 58J50 PDF BibTeX XML Cite \textit{R. Beals} and \textit{N. K. Stanton}, Commun. Partial Differ. Equations 12, 351--413 (1987; Zbl 0615.58033) Full Text: DOI
Diaz, Ricardo L. Necessary conditions for subellipticity of \(\square _ b\) on pseudoconvex boundaries. (English) Zbl 0586.32025 Commun. Partial Differ. Equations 11, 1-61 (1986). Reviewer: M.Muro MSC: 32W05 35N15 32T99 58J10 PDF BibTeX XML Cite \textit{R. L. Diaz}, Commun. Partial Differ. Equations 11, 1--61 (1986; Zbl 0586.32025) Full Text: DOI
Stanton, Nancy K.; Tartakoff, David S. The real analytic and Gevrey regularity of the heat kernel for \(\square _ b\). (English) Zbl 0586.32026 Pseudodifferential operators and applications, Proc. Symp., Notre Dame/Indiana 1984, Proc. Symp. Pure Math. 43, 247-259 (1985). Reviewer: D.Yang MSC: 32W05 35N15 32C05 32J99 PDF BibTeX XML
Rudin, Walter Function theory in the unit ball of \({\mathbb{C}}^ n\). (Teoriya funktsij v edinichnom share iz \({\mathbb{C}}^ n)\). Transl. from the English. (Russian) Zbl 0597.32001 Moskva: Izdatel’stvo ”Mir”. 455 p. R. 4.10 (1984). MSC: 32-02 32A10 32A40 32A38 32A22 32A25 32W05 32A35 32E35 32U05 32M05 32H99 PDF BibTeX XML
Jerison, David S. Boundary regularity in the Dirichlet problem for \(\square_ b\) on CR manifolds. (English) Zbl 0544.35069 Commun. Pure Appl. Math. 36, 143-181 (1983). Reviewer: C.Zuily MSC: 35N15 32V40 35C20 32W05 35J70 PDF BibTeX XML Cite \textit{D. S. Jerison}, Commun. Pure Appl. Math. 36, 143--181 (1983; Zbl 0544.35069) Full Text: DOI
Donnelly, Harold; Fefferman, Charles \(L^ 2\)-cohomology and index theorem for the Bergman metric. (English) Zbl 0532.58027 Ann. Math. (2) 118, 593-618 (1983). MSC: 58J10 32T99 32A25 53C55 53C15 58J60 58A14 35N15 55N20 35C20 58J20 PDF BibTeX XML Cite \textit{H. Donnelly} and \textit{C. Fefferman}, Ann. Math. (2) 118, 593--618 (1983; Zbl 0532.58027) Full Text: DOI
Stein, Elias M. An example of the Heisenberg group. (English) Zbl 0497.35069 Journ. Équ. Dériv. Partielles, Saint-Jean-De-Monts 1982, Exp. No. 15, 3 p. (1982). MSC: 35N15 32W05 65H10 35A07 PDF BibTeX XML Full Text: Numdam EuDML
Tartakoff, D. S. Elementary proofs of analytic hypoellipticity for a wave operator and the (partial d)–Neumann problem. (English) Zbl 0497.35023 Astérisque 89-90, 85-116 (1981). MSC: 35H10 35N15 PDF BibTeX XML
Grigis, A. Propagation des singularites au bord d’ouverts de \(C^ n\). (French) Zbl 0472.58021 Commun. Partial Differ. Equations 6, 689-717 (1981). MSC: 58J47 58J40 35N15 58J15 PDF BibTeX XML Cite \textit{A. Grigis}, Commun. Partial Differ. Equations 6, 689--717 (1981; Zbl 0472.58021) Full Text: DOI
Geller, Daryl The Laplacian and the Kohn Laplacian for the sphere. (English) Zbl 0507.58049 J. Differ. Geom. 15, 417-435 (1980). MSC: 58J60 32W05 35N15 32K15 65H10 PDF BibTeX XML Cite \textit{D. Geller}, J. Differ. Geom. 15, 417--435 (1980; Zbl 0507.58049) Full Text: DOI
Rudin, Walter Function theory in the unit ball of \(\mathbb{C}^n\). (English) Zbl 0495.32001 Grundlehren der mathematischen Wissenschaften, Bd. 241. New York-Heidelberg-Berlin: Springer-Verlag. xiii, 436 p. DM 79.50; $ 46.90 (1980). Reviewer: C. Andreian Cazacu MSC: 32-02 32A10 32A40 32A38 32A22 32A25 32A35 32E35 32U05 32W05 32M05 32H99 PDF BibTeX XML
Luk, Hing-Sun Affine connections and defining functions of real hypersurfaces in \(C^n\). (English) Zbl 0441.53026 Trans. Am. Math. Soc. 259, 579-588 (1980). MSC: 53C05 53B05 32T99 35N15 PDF BibTeX XML Cite \textit{H.-S. Luk}, Trans. Am. Math. Soc. 259, 579--588 (1980; Zbl 0441.53026) Full Text: DOI
Rothschild, Linda Preiss; Tartakoff, David Parametrices with \(C^\infty\) error for \(\square_b\) and operators of Hörmander type. (English) Zbl 0409.35021 Partial differential equations and geometry, Proc. Park City Conf. 1977, Lect. Notes Pure Appl. Math. 48, 255-271 (1979). MSC: 35H10 35B65 35N15 PDF BibTeX XML