Optimal \(L^ p\) estimates for the \(\bar \partial\)-equation on complex ellipsoids in \(\mathbb{C}^ n\)

DOI10.1007/BF03026542zbMath0789.32011MaRDI QIDQ1313569

Daowei Ma, Zhenhua Chen, Steven G. Krantz

Publication date: 7 February 1994

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155864

zbMATH Keywords

ellipsoids\(\overline\partial\)-equation\(L^ 2\)-estimates

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items

\(C^k\)-estimates for \(\bar{\partial}\)-equation on certain convex domains of infinite type in \(\mathbb{C}^n\), L^p estimates for the $\bar\partial$-equation on a class of infinite type domains, Sharp estimates for \(\bar\partial\) on convex domains of finite type, Optimal Lipschitz estimates for the \(\bar\partial\) equation on a class of convex domains, Weighted and boundary \(L^{p}\) estimates for solutions of the \(\overline{\partial}\)-equation on lineally convex domains of finite type and applications, Cauchy-Riemann equation in real ellipsoids of \(\mathbb{C}^n\), \(C^k\)-regularity for \(\bar{\partial}\)-equations for a class of convex domains of infinite type in \(\mathbb{C}^2 \), Unnamed Item, Hölder and \(L^p\) estimates for the \({\bar{\partial }}\)-equation in a class of convex domains of infinite type in \({\mathbb{C}}^n\), \(L^p\) estimates for \(\overline\partial\)-equation on generalized complex ellipsoids

Cites Work

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• Holomorphic functions of bounded mean oscillation and mapping properties of the Szegö projection
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• Estimates for the ∂̄-Neumann problem for pseudoconvex domains in C ² of finite type
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• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Hölder and L^p estimates for solutions of ∂u = f in strongly pseudoconvex domains
• Integral Representation Formulas and $L^p$-Estimates for the $\bar{\partial}$-Equation.