On Hölder estimates with loss of order one for the \(\bar{\partial}\) equation on a class of convex domains of infinite type in \(\mathbb {C}^{3}\)

DOI10.1007/s40306-018-0288-6zbMath1419.32009OpenAlexW2888168364MaRDI QIDQ2000821

Ly Kim Ha

Publication date: 28 June 2019

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

Full work available at URL: https://doi.org/10.1007/s40306-018-0288-6

zbMATH Keywords

Hölder estimates\(\bar {\partial }\)-equationHenkin solution operatorinfinite-type domains

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Analytical consequences of geometric convexity (vanishing theorems, etc.) (32F32) Pseudoconvex domains (32T99)

Cites Work

• On supnorm estimates for \(\bar \partial\) on infinite type convex domains in \(\mathbb C^{2}\)
• Hölder and \(L^ p\)-estimates for the \({\bar\partial}\)-equation in some convex domains with real-analytic boundary
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• Subelliptic estimates and regularity of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\bf \bar{\partial}$\end{document} at the boundary of a Q-pseudoconvex domain of finite type
• Estimates for regularity of the tangential \documentclass{article}\usepackage{amssymb,amsmath}\begin{document}\pagestyle{empty}$\bar{\partial }$\end{document}-system
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• INTEGRAL REPRESENTATION OF FUNCTIONS IN STRICTLY PSEUDOCONVEX DOMAINS AND APPLICATIONS TO THE $ \overline{\partial}$-PROBLEM
• Hölder regularity for \(\overline\partial\) on the convex domains of finite strict type.
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