Differentiability of the Bergman kernel and pseudo-local estimates

DOI10.1007/BF01164021zbMath0594.32025MaRDI QIDQ1076857

Steven R. Bell

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173750

zbMATH Keywords

Bergman kernel functionpseudoconvex domainsBergman projectorapproximating domainspseudo-local estimates

Mathematics Subject Classification ID

(q)-convexity, (q)-concavity (32F10) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Pseudoconvex domains (32T99)

Related Items

Extension of \(CR\) structures on three dimensional compact pseudoconvex CR manifolds ⋮ Duality and approximation of Bergman spaces ⋮ Regularity of CR mappings ⋮ Local extension of boundary holomorphic forms on real hypersurfaces in \(\mathbb C^{n}\) ⋮ L2-Sobolev theory for the complex Green operator ⋮ The boundary behavior of holomorphic functions ⋮ A note on L2-boundary integrals of the Bergman kernel ⋮ Comparison of the Bergman and Szegö kernels ⋮ Axler-Zheng type theorem on a class of domains in \(\mathbb C^n\) ⋮ A counterexample to the differentiability of the Bergman kernel function ⋮ ON DISCONTINUITY OF THE BERGMAN KERNEL FUNCTION ⋮ Further remarks on the higher dimensional Suita conjecture ⋮ Regularity of the $\overline\partial$-Neumann Problem ⋮ Peak points for pseudoconvex domains: A survey ⋮ Unique continuation theorems for the \(\bar \partial\)-operator and applications ⋮ Local Boundary Regularity of the Szego Projection and Biholomorphic Mappings of Non-Pseudoconvex Domains ⋮ Extension of complex structures on weakly pseudoconvex compact complex manifolds with boundary ⋮ Domains with hyperbolic orbit accumulation boundary points ⋮ Analytic discs, plurisubharmonic hulls, and non-compactness of the \(\bar\partial\)-Neumann operator ⋮ On a holomorphic family of Stein manifolds with strongly pseudoconvex boundaries ⋮ Weakly pseudoconvex domains with non-compact automorphism groups ⋮ Sobolev estimates for the local extension of ∂̄_{𝑏}-closed (0,1)-forms on real hypersurfaces in ℂⁿ with two positive eigenvalues ⋮ The complex Green operator on CR-submanifolds of $\mathbb{C}^{n}$ of hypersurface type: Compactness ⋮ Berezin regularity of domains in $\mathbb {C}^n$ and the essential norms of Toeplitz operators ⋮ Unnamed Item ⋮ Strong Stein neighbourhood bases

Cites Work

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• Boundary invariants of pseudoconvex domains
• Subelliptic estimates for the \({\bar \partial}\)-Neumann problem on pseudoconvex domains
• Biholomorphic mappings and the \(\overline\partial\)-problem
• Real hypersurfaces, orders of contact, and applications
• Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions
• Global Regularity for $\overline \partial$ on Weakly Pseudo-Convex Manifolds

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