Solution operators for the \(\bar\partial\)-equation on non-transversal intersections of strictly pseudoconvex domains
type: Item
instance of: scholarly article
title: Solution operators for the \(\bar\partial\)-equation on non-transversal intersections of strictly pseudoconvex domains
zbMATH Open document ID: 0748.32010
DOI: 10.1007/BF01445231
author: Klaus Peters
published in: Mathematische Annalen
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/164890
review text: Solution operators for the inhomogeneous Cauchy-Riemann equation on non- transversal intersections of strictly pseudoconvex domains are constructed. We consider arbitrary intersections of three domains, \(D=D'\cap\Omega\cap D''\), where \(D'\) and \(D''\) are strictly pseudoconvex domains with not necessarily smooth boundary and \(\Omega\) is a transversal intersection of finitely many strictly pseudoconvex domains with smooth boundaries. For such domains we construct operators with uniform estimates and operators which map the \(C^{2k}\)-forms on \(\overline D\) which admit extensions to \(C^{2k}\)-forms on a neighbourhood of \(\overline D\), continuously into the space of \(C^k\)-forms on \(\overline D\). It is not clear whether one can avoid this loss of regularity or not.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 59942
zbMATH Keywords: Cauchy-Riemann equation
zbMATH Keywords: integral representations
zbMATH Keywords: pseudoconvex domains
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 59942