Randregularität des \({\bar\partial}\)-Problems für die Halbkugel in \({\mathbb{C}}^ n\). (Boundary regularity of the \({\bar\partial}\)-problem for the half ball in \({\mathbb{C}}^ n)\)
type: Item
instance of: scholarly article
title: Randregularität des \({\bar\partial}\)-Problems für die Halbkugel in \({\mathbb{C}}^ n\). (Boundary regularity of the \({\bar\partial}\)-problem for the half ball in \({\mathbb{C}}^ n)\)
zbMATH Open document ID: 0592.32016
DOI: 10.1007/BF01186647
author: Joachim Michel
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155140
review text: The author proves \(C^ k\) regularity estimates for the \({\bar \partial}\)-operator on the domain \(\{z\in {\mathbb{C}}^ n: Re z_ n>0,\quad | z| <1\}.\) As the author points out, such a domain is of interest because it is a mixture of the strongly pseudoconvex (ball) case and the Levi flat (polydisc) case, both of which are well understood. The integral kernels which arise involve interesting mixtures of singularities. Part of the work is to construct new integral formulas which give good regularity for \(C^ k\), \(k>1.\) It seems likely that the same proof will give results for a strongly convex domain intersected with a half space. With suitable modifications, the result ought to hold for the intersection of a general strongly pseudoconvex domain with a half space.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 35N15
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 3950980
zbMATH Keywords: inhomogeneous Cauchy-Riemann equations
zbMATH Keywords: uniform estimates
zbMATH Keywords: regularity estimates for the \({\bar \partial }\)-operator
zbMATH Keywords: integral formulas
zbMATH Keywords: strongly pseudoconvex domain
reviewed by: Steven G. Krantz
MaRDI profile type: Publication
cites work: Fundamental solutions in complex analysis. I. The Cauchy Riemann operator
cites work: Lösungsoperatoren für den Cauchy-Riemann-Komplex mit \(\mathcal C^K\)- Abschätzungen
OpenAlex ID: W2912291736
description: scientific article; zbMATH DE number 3950980