Behavior of the Bergman projection on the Diederich-Fornæss worm
type: Item
instance of: scholarly article
title: Behavior of the Bergman projection on the Diederich-Fornæss worm
zbMATH Open document ID: 0779.32013
DOI: 10.1007/BF02392975
author: David E. Barrett
published in: Acta Mathematica
publication date: 1993-02-25T00:00:00Z
review text: Define \(\Omega=\{(z_ 1,z_ 2)/| z_ 1+e^{i\log z_ 2\overline z_ 2}|^ 2<1-\varphi(\log z_ 2\overline z_ 2)\) where \(\varphi\) is a smooth nonnegative even function choosen such that \(\Omega\) is a smooth bounded, connected pseudoconvex domain, and moreover \(\varphi^{- 1}(0)=[-\beta+\pi/2,\beta-\pi/2]\). The following result is proven: Theorem. The Bergmann projection operator attached to \(\Omega\) does not map \(W^ k(\Omega)\) into \(W^ k(\Omega)\) when \(k\geq/(2\beta-\pi)\). This settles negatively a long standing problem about the behaviour of the Bergman projection for weakly pseudoconvex domains.
reviewed by: Nicolae Mihalache
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 109062
zbMATH Keywords: Soboloev spaces
zbMATH Keywords: Bergman projection
zbMATH Keywords: weakly pseudoconvex domains
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 109062