Bessel capacity, Hausdorff content and the tangential boundary behavior of harmonic functions
type: Item
instance of: scholarly article
title: Bessel capacity, Hausdorff content and the tangential boundary behavior of harmonic functions
zbMATH Open document ID: 0869.31006
author: Hiroaki Aikawa
published in: Hiroshima Mathematical Journal
publication date: 1997-08-19T00:00:00Z
review text: The main result gives some comparison of the Bessel capacity and the Hausdorff content. It is shown that the Bessel capacity of \[ \tilde{E}_{\gamma, c}= \bigcap_{x\in E}B(x,c\delta _E(x)^{\gamma}) \] for \(E \subset \mathbb{R}^n\) can be estimated by the Hausdorff content of \(E\). This is applied to the investigation of the tangential boundary behaviour of harmonic functions in the upper half plane. The results generalize and improve the previous paper [\textit{H. Aikawa} and \textit{A. A. Borichev}, Trans. Am. Math. Soc. 348, 1013-1030 (1996; Zbl 0856.31004)].
reviewed by: S. G. Samko
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 31B25
zbMATH DE Number: 986961
zbMATH Keywords: Riesz capacity
zbMATH Keywords: Bessel capacity
zbMATH Keywords: Hausdorff content
zbMATH Keywords: tangential boundary behaviour
zbMATH Keywords: harmonic functions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206127368
OpenAlex ID: W1536186493
DOI: 10.32917/HMJ/1206127368
description: scientific article; zbMATH DE number 986961