Representations of bounded harmonic functions
type: Item
instance of: scholarly article
title: Representations of bounded harmonic functions
zbMATH Open document ID: 0728.31003
DOI: 10.1007/BF02384334
published in: Arkiv för Matematik
publication date: 1991-01-01T00:00:00Z
review text: The paper deals with open subsets D of \({\mathbb{R}}^ d\), \(d\geq 2\) (called Poissonian), where every bounded harmonic function on D is a Poisson integral of a bounded function on its boundary. The intersection of two Poissonian open sets is proved to be Poissonian and a sufficient condition for the union of two Poissonian sets to be Poissonian is given. The authors also give some necessary and sufficient conditions for an open set to be Poissonian, and in particular a necessary and sufficient condition for a Greenian to be Poissonian in terms of its Martin boundary.
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 31C35
zbMATH DE Number: 4202681
zbMATH Keywords: Poisson integral representation
zbMATH Keywords: bounded harmonic function
zbMATH Keywords: Poissonian open sets
author: Thomas Mountford
author: Sidney C. Port
MaRDI profile type: Publication
cites work: Q3483547
cites work: Harmonic measures supported on curves
cites work: A characterization of Poissonian domains
cites work: Q3048019
full work available at URL: https://doi.org/10.1007/bf02384334
OpenAlex ID: W2084742718
description: scientific article; zbMATH DE number 4202681