Exact regularity of Bergman, Szegö and Sobolev space projections in non pseudoconvex domains
type: Item
instance of: scholarly article
title: Exact regularity of Bergman, Szegö and Sobolev space projections in non pseudoconvex domains
zbMATH Open document ID: 0573.46018
DOI: 10.1007/BF01162025
author: Emil J. Straube
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173720
review text: Let \(\Omega\) be a smooth, bounded Reinhard domain. It is shown that the Bergman and the Szegö projections, as well as the higher order Sobolev space analogues of the Bergman projection, all satisfy exact regularity estimates in Sobolev norms. These estimates were previously known only under the additional assumptions of pseudoconvexity and completeness of \(\Omega\). For the case of the Bergman projection, it is shown that exact regularity is actually true more generally on domains with ''transverse symmetries''.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 3914979
zbMATH Keywords: Reinhardt domain
zbMATH Keywords: Bergman and the Szegö projections
zbMATH Keywords: higher order Sobolev space analogues of the Bergman projection
zbMATH Keywords: regularity estimates in Sobolev norms
zbMATH Keywords: pseudoconvexity and completeness
zbMATH Keywords: transverse symmetries
MaRDI profile type: Publication
cites work: Regularity of the Bergman projection on domains with transverse symmetries
cites work: Regularity of the Bergman projection and local geometry of domains
cites work: Action of the Automorphisms of a Smooth Domain in C n
cites work: Holomorphic reproducing kernels in Reinhardt domains
cites work: Q3218379
cites work: Sobolev Space Projections In Strictly Pseudoconvex Domains
cites work: Variation of the Bergman kernel by cutting a hole
cites work: Q3924489
cites work: Q5628582
cites work: Orthogonal projections onto subspaces of the harmonic Bergman space
description: scientific article; zbMATH DE number 3914979