On Sobolev and capacitary inequalities for contractive Besov spaces over \(d\)-sets
type: Item
instance of: scholarly article
title: On Sobolev and capacitary inequalities for contractive Besov spaces over \(d\)-sets
zbMATH Open document ID: 1017.31005
DOI: 10.1023/A:1020552322198
author: Masatoshi Fukushima
author: Toshihiro Uemura
published in: Potential Analysis
publication date: 2003-04-27T00:00:00Z
review text: The authors derive Sobolev inequalities for Besov spaces from a metric property of the Bessel capacity on \(\mathbb{R}^n\). First, they extend Kaimanovitch's result on the equivalence of Sobolev and capacity inequalities for contractive \(p\)-norms in a general setting allowing unbounded Lévy kernels. Then they apply a simple part of the Jonsson-Wallin trace theorem to Besov spaces.
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 1901234
zbMATH Keywords: Besov spaces
zbMATH Keywords: \(d\)-sets
zbMATH Keywords: contractive \(p\)-norm
zbMATH Keywords: Sobolev inequality
zbMATH Keywords: capacitary inequality
reviewed by: Sophia L. Kalpazidou
MaRDI profile type: Publication
full work available at URL: a:1020552322198
OpenAlex ID: W43163492
description: scientific article; zbMATH DE number 1901234