Jensen measures and boundary values of plurisubharmonic functions
type: Item
instance of: scholarly article
title: Jensen measures and boundary values of plurisubharmonic functions
zbMATH Open document ID: 1021.32014
DOI: 10.1007/BF02388798
author: Frank Wikström
published in: Arkiv för Matematik
publication date: 2003-06-16T00:00:00Z
review text: For a bounded domain \(\Omega\), let \({\mathcal J}_z^c\) and \({\mathcal J}_z\) denote the collections of all Jensen measures with barycentre \(z\in\overline\Omega\) for continuous (resp., upper bounded) plurisubharmonic functions in \(\Omega\). It is shown that \({\mathcal J}_z\) can be a proper subset of \({\mathcal J}_z^c\), however these two classes coincide for all B-regular domains \(\Omega\). The proof of the latter result is based on an approximation theorem for upper bounded plurisubharmonic functions in a B-regular domain \(\Omega\) by continuous plurisubharmonic functions on \(\overline\Omega\). Conversely, if a bounded hyperconvex domain \(\Omega\) is such that \({\mathcal J}_z ={\mathcal J}_z^c\) for all \(z\), then \(\Omega\) possesses this approximation property. The author gives also an exact characterization, in terms of Jensen measures, of those continuous functions on \(\partial\Omega\) that are boundary values of continuous plurisubharmonic functions.
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 46E27
Mathematics Subject Classification ID: 31C10
zbMATH DE Number: 1928899
zbMATH Keywords: Jensen measures
zbMATH Keywords: plurisubharmonic functions
zbMATH Keywords: boundary values
zbMATH Keywords: hyperconvexity
zbMATH Keywords: B-regular domains
zbMATH Keywords: approximation
MaRDI profile type: Publication
cites work: Q4351904
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description: scientific article; zbMATH DE number 1928899