On separately subharmonic functions (Lelong's problem)
type: Item
instance of: scholarly article
title: On separately subharmonic functions (Lelong's problem)
zbMATH Open document ID: 1227.31006
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2011-10-11T00:00:00Z
full work available at URL: https://eudml.org/doc/219681
review text: We will call a function \(u:\mathbb{R}^{n}\times \mathbb{R}^{m}\rightarrow \mathbb{R}\) separately subharmonic-harmonic if \(u(\cdot ,y)\) is subharmonic for each \(y\), and \(u(x,\cdot )\) is harmonic for each \(x\). The author shows that \(u\) can then be represented locally in the form \(u^{\ast }+U\), where \(U\) is jointly subharmonic, \(u^{\ast }\) is separately subharmonic-harmonic, and \(u^{\ast }\) is jointly harmonic outside some nowhere dense set. The question of whether \(u\) itself is jointly subharmonic remains open.
reviewed by: Stephen J. Gardiner
Mathematics Subject Classification ID: 31B05
zbMATH DE Number: 5956568
zbMATH Keywords: harmonic function
zbMATH Keywords: subharmonic function
zbMATH Keywords: separately subharmonic function
author: A. S. Sadullaev
MaRDI profile type: Publication
OpenAlex ID: W2314721994
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DOI: 10.5802/AFST.1311
description: scientific article; zbMATH DE number 5956568