On weighted \(L^p\)-Sobolev estimates for solutions of the \(\overline{\partial}\)-equation on linearly convex domains of finite type and application

DOI10.1007/s40306-024-00530-yMaRDI QIDQ6597141

Philippe Charpentier, Yves Dupain

Publication date: 3 September 2024

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

zbMATH Keywords

weighted Bergman projection\(\overline{\partial}\)-equationconvex domains of finite type

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Finite-type domains (32T25) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Cites Work

• Unnamed Item
• Estimates for solutions of the \(\bar\partial\)-equation and application to the characterization of the zero varieties of the functions of the Nevanlinna class for lineally convex domains of finite type
• Weighted and boundary \(L^{p}\) estimates for solutions of the \(\overline{\partial}\)-equation on lineally convex domains of finite type and applications
• \(C^{k}\)-estimates for the \(\bar\partial\)-equation on convex domains of finite type
• Sobolev and Hölder estimates for \(\overline{\partial}\) on bounded convex domains in \(\mathbb{C}^2\)
• Henkin-Ramirez kernels with weight factors
• Optimal Sobolev estimates for \(\bar\partial\) on convex domains of finite type
• Lineally convex domains of finite type: holomorphic support functions
• \(C^k\)-estimates for the \(\overline\partial_b\)-equation on convex domains of finite type
• On estimates for weighted Bergman projections
• Estimates for weighted Bergman projections on pseudo-convex domains of finite type in ℂⁿ

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