On local harmonic majorants of subharmonic functions
type: Item
instance of: scholarly article
title: On local harmonic majorants of subharmonic functions
zbMATH Open document ID: 0358.31001
DOI: 10.1007/BF02813306
published in: Journal d'Analyse Mathématique
publication date: 1977-01-01T00:00:00Z
review text: In this note the author proves that a function \(f\), subharmonic in the interior \(S\) of a compact bordered Riemann surface, which admits a local harmonic majorant at each point of the boundary \(B\) of the surface, must then have a harmonic majorant in the interior \(S\). The author's proof of this result makes use of the proof by \textit{P. M.Gauthier} and \textit{W. Hengartner} [J. Analyse math. 26, 405--412 (1973; Zbl 0079.31001)] of that same result where \(S\) is the unit disc. The author offers a second proof of the result for the special case that is more elementary than the first one. Then the author uses the second proof to show that a function \(F\) meromorphic in \(S\) above \(S\) of bounded characteristic there if and only if \(F\) is of bounded characteristic at each point of the boundary \(B\) (i.e., \(F\) is locally of bounded characteristic). This last result is essentially due to \textit{M. Heins} [J. Analyse math. 18, 121--131 (1967; Zbl 0152.06902)] but the present proof seems to be a much more elementary one than that due to Heins.
Mathematics Subject Classification ID: 31A05
Mathematics Subject Classification ID: 30D30
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 3558176
author: Shōji Kobayashi
reviewed by: Maxwell O. Reade
MaRDI profile type: Publication
cites work: Local harmonic majorants of functions subharmonic in the unit disc
cites work: The boundary values of meromorphic functions having bounded Nevanlinna characteristic
cites work: The boundary values of analytic and harmonic functions
full work available at URL: https://doi.org/10.1007/bf02813306
OpenAlex ID: W2011943495
description: scientific article; zbMATH DE number 3558176