Extensions and imbeddings
type: Item
instance of: scholarly article
title: Extensions and imbeddings
zbMATH Open document ID: 0924.46031
author: Pekka Koskela
published in: Journal of Functional Analysis
publication date: 1999-03-22T00:00:00Z
review text: Let \(D\) be a bounded domain in \(\mathbb{R}^n\). It is the main aim of this paper to clarify the intimate relationship between the following two properties: (i) Sobolev's embedding \(W^1_p(D)\subset C^\alpha(D)\), \(\alpha=1-{n\over p}\), \(p>n\), (ii) there is a bounded extension operator from the Sobolev space \(W^1_q(D)\) into \(W^1_q(\mathbb{R}^n)\), where \(q>p\). In particular, the dependence of the extension property on \(p\) is discussed.
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1268051
zbMATH Keywords: Sobolev's embedding
zbMATH Keywords: bounded extension
zbMATH Keywords: extension property
MaRDI profile type: Publication
full work available at URL: jfan.1998.3331
OpenAlex ID: W1983145077
Wikidata QID: Q112014159
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DOI: 10.1006/JFAN.1998.3331
description: scientific article; zbMATH DE number 1268051