Estimates for the Bergman and Szegö kernels in certain weakly pseudoconvex domains

DOI10.1090/S0273-0979-1988-15598-XzbMath0642.32014OpenAlexW2019212463MaRDI QIDQ3784394

Elias M. Stein, Stephen Wainger, Alexander Nagel, Jean-Pierre Rosay

Publication date: 1988

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1988-15598-x

zbMATH Keywords

estimatesBergman kernelSzegö kernelsubharmonic polynomials

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Boundary behavior of holomorphic functions of several complex variables (32A40) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Holomorphic functions of several complex variables (32A10)

Related Items

Comparing the Bergman and the Szegö projections ⋮ Hölder estimates on domains of complex dimension two and on three- dimensional CR manifolds ⋮ Estimates for the parametrix of the Kohn Laplacian on certain domains ⋮ On uniform large-scale volume growth for the Carnot-Carathéodory metric on unbounded model hypersurfaces in \(\mathbb{C}^2\) ⋮ On the non-analytic examples of Christ and Geller ⋮ Weighted estimates for the Bergman projection on the Hartogs triangle ⋮ $L^p$ estimates for the Bergman projection on some Reinhardt domains ⋮ An application of John ellipsoids to the Szegő kernel on unbounded convex domains ⋮ Weak‐type estimates for the Bergman projection on the polydisc and the Hartogs triangle ⋮ Solution of the tangential Kohn Laplacian on a class of non-compact CR manifolds ⋮ Estimates for the Szegö and Henkin kernels in Hardy classes on certain unbounded weakly pseudoconvex domains ⋮ On the growth of the Bergman metric near a point of infinite type ⋮ Local analyticity for the \(\bar {\partial{}}\)-Neumann problem and \({\square{}}_ b\) -- some model domains without maximal estimates ⋮ On the growth of the Bergman kernel near an infinite-type point ⋮ Solving the Kohn Laplacian on asymptotically flat CR manifolds of dimension 3

Cites Work

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• Balls and metrics defined by vector fields. I: Basic properties
• Hypoelliptic second order differential equations
• A pseudo-convex domain not admitting a holomorphic support function
• Boundary behavior of functions holomorphic in domains of finite type