Removable sets for harmonic functions
type: Item
instance of: scholarly article
title: Removable sets for harmonic functions
zbMATH Open document ID: 0751.31001
author: David C. Ullrich
published in: Michigan Mathematical Journal
publication date: 1992-09-27T00:00:00Z
review text: The author shows that a compact subset \(K\subset\mathbb{R}^ d\), \(d\geq 2\), is removable for a harmonic function in the Zygmund class if and only if \(m_{d-1}(K)=0\); here \(m_{d-1}\) dennotes \((d-1)\)-dimensional Hausdorff measure. The author's results imply a simpler proof of Carleson's theorem for removable sets in the class \(\text{Lip} \alpha\), \(0<\alpha<1\), [see \textit{L. Carleson}, Selected problems on exceptional sets (1967; Zbl 0189.109)].
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 31C05
zbMATH DE Number: 59887
zbMATH Keywords: Zygmund class
zbMATH Keywords: Carleson's theorem
zbMATH Keywords: removable sets
reviewed by: Miroslav Brzezina
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004395
OpenAlex ID: W1969271709
DOI: 10.1307/MMJ/1029004395
description: scientific article; zbMATH DE number 59887