Complete Hartogs domains in \({\mathbb{C}}^ 2\) have regular Bergman and Szegö projections
type: Item
instance of: scholarly article
title: Complete Hartogs domains in \({\mathbb{C}}^ 2\) have regular Bergman and Szegö projections
zbMATH Open document ID: 0653.32023
DOI: 10.1007/BF01214907
author: Harold P. Boas
author: Emil J. Straube
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174064
review text: The Bergman and Szegö projections do not preserve regularity of functions in all smooth bounded domains. The known counterexamples, constructed by Barrett and by Barrett and Fornæss, are certain (non- pseudoconvex) domains in \({\mathbb{C}}^ 2\) that are Hartogs domains. This paper delimits the nature of the obstruction to regularity exhibited by these domains. It is shown that the Bergman and Szegö projections exactly preserve differentiability of functions as measured by Sobolev norms in smooth bounded Hartogs domains in \({\mathbb{C}}^ 2\) that are complete (but not necessarily pseudoconvex). Consequently, biholomorphic mappings between such domains extend smoothly to the boundaries.
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 32E35
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 4065415
zbMATH Keywords: Szegö projections
zbMATH Keywords: regularity
zbMATH Keywords: Hartogs domains
zbMATH Keywords: biholomorphic mappings
zbMATH Keywords: Bergman projections
Wikidata QID: Q57376118
reviewed by: Emil J. Straube
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4065415