The \(\overline\partial\)-Neumann operator on Lipschitz pseudoconvex domains with plurisubharmonic defining functions
type: Item
instance of: scholarly article
title: The \(\overline\partial\)-Neumann operator on Lipschitz pseudoconvex domains with plurisubharmonic defining functions
zbMATH Open document ID: 1020.32030
DOI: 10.1215/S0012-7094-01-10832-6
author: Joachim Michel
author: Mei-Chi Shaw
published in: Duke Mathematical Journal
publication date: 2002-10-27T00:00:00Z
review text: If \(D\) is a bounded pseudoconvex Lipschitz domain in \(\mathbb{C}^n\) with a plurisubharmonic Lipschitz defining function, the authors prove that the \(\overline\partial\)-Neumann operator and the canonical Kohn solution operator of the \(\overline\partial\)-equation are bounded from the Sobolev space \(H^{1/2}(D)\) to itself. In a more general setting a slightly weaker result has been obtained by \textit{Bo Berndtsson} and \textit{Ph. Charpentier} [Math. Z. 235, 1-10 (2000; Zbl 0969.32015)] who proved that the Kohn operator and the Bergman projection are bounded on \(H^s\) for \(s< \eta/2\) provided that \(D\) has a defining function \(\rho\) such that \(-(-\rho)^\eta\) is plurisubharmonic.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32U10
Mathematics Subject Classification ID: 35N15
zbMATH DE Number: 1820826
zbMATH Keywords: bounded pseudoconvex Lipschitz domain in \(\mathbb{C}^n\)
zbMATH Keywords: plurisubharmonic Lipschitz defining function
zbMATH Keywords: \(\overline\partial\)-Neumann operator
zbMATH Keywords: canonical Kohn solution operator
reviewed by: P-A Mazet
MaRDI profile type: Publication
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full work available at URL: s0012-7094-01-10832-6
OpenAlex ID: W2022046249
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description: scientific article; zbMATH DE number 1820826