Projection theorems for harmonic measure in NTA domains
type: Item
instance of: scholarly article
title: Projection theorems for harmonic measure in NTA domains
zbMATH Open document ID: 0970.31007
DOI: 10.1023/A:1008791022455
author: Peter M. Knopf
published in: Potential Analysis
publication date: 2001-02-18T00:00:00Z
review text: Let \(D\) be an NTA domain, and \(E\subset D\) be a closed subset. It is assumed that there exists a kind of projection \(P^{x_0}(E)\), depending on a fixed point \(x_0\), of \(E\) onto the boundary of \(D\). The projection is a sort of generalization of the radial projection. The main result of this paper is that the harmonic measure of the set \(\partial E\) with respect to the domain \(D\setminus E\) can be estimated from below with the harmonic measure of the set \(P^{x_0}(E)\) times a constant which is independent of \(E\) but depending on \(x_0\).
Mathematics Subject Classification ID: 31C05
zbMATH DE Number: 1565491
zbMATH Keywords: harmonic measure
zbMATH Keywords: projection theorems
zbMATH Keywords: NTA domains
MaRDI profile type: Publication
full work available at URL: a:1008791022455
OpenAlex ID: W15552016
description: scientific article; zbMATH DE number 1565491