Mapping properties of the Bergman projection on convex domains of finite type

DOI10.1215/S0012-7094-94-07307-9zbMath0801.32008OpenAlexW1515167977MaRDI QIDQ1325156

Elias M. Stein, Jeffery D. Mcneal

Publication date: 1 December 1994

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-94-07307-9

zbMATH Keywords

Sobolev spaceLipschitz spaceBergman projectionbounded convex domainsBerman kernel

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hölder estimates on domains of complex dimension two and on three- dimensional CR manifolds
• Szegö kernels on pseudoconvex domains with one degenerate eigenvalue
• Estimates for the Bergman and Szegö kernels in \({\mathbb{C}}^ 2\)
• Boundary behavior of the Bergman kernel function in \({\mathbb{C}}^ 2\)
• Estimates for the Bergman and Szegö projections on strongly pseudo-convex domains
• The Bergman projection as a singular integral operator
• Estimates on the Bergman kernels of convex domains
• Hölder estimates on CR manifolds with a diagonalizable Levi form
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• On a Theorem of Stein
• Estimates for the ∂̄-Neumann problem for pseudoconvex domains in C ² of finite type
• Regularity Properties of the ∂ b Equation on Weakly Pseudoconvex CR Manifolds of Dimension 3
• Holomorphic Lipschitz Functions in Pseudoconvex Domains
• Singular integrals and estimates for the Cauchy-Riemann equations