The Bergman projection and weighted $C^{k}$ estimates for the canonical solution to the $\bar{\partial}$ problem on non-smooth domains

DOI10.1090/S0002-9947-2011-05277-3zbMath1229.32009arXiv0903.4087OpenAlexW1783728835MaRDI QIDQ3020326

Dariush Ehsani

Publication date: 4 August 2011

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

Full work available at URL: https://arxiv.org/abs/0903.4087

zbMATH Keywords

Bergman projectionboundary with nondegenerate critical pointsstrictly psudoconvex domain

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Cites Work

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• Integral representations on nonsmooth domains
• Weighted \(C^{k}\) estimates for a class of integral operators on non-smooth domains
• Estimates for a class of integral operators and applications to the \({\bar\partial}\)-Neumann-problem
• Solution of the \({\bar \partial}\)-equation with uniform estimates on strictly q-convex domains with non-smooth boundary
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Lp -estimates for the Bergman projection on strictly pseudoconvex nonsmooth domains