Sobolev extension domains on metric spaces of homogeneous type.
type: Item
instance of: scholarly article
title: Sobolev extension domains on metric spaces of homogeneous type.
zbMATH Open document ID: 1082.46024
author: Petteri Harjulehto
published in: Real Analysis Exchange
publication date: 2004-08-06T00:00:00Z
review text: The author proves that there exists a bounded linear extension operator \[ \text{Ext}: M^{1,p}(\Omega,d,\mu)\to M^{1,p}(\Omega, d,\mu) \] such that \(\text{Ext}(u)|_\Omega= u\), where \(M^{1,p}(\Omega,d,\mu)\) is the Hajlasz space. Here, \((X,d,\mu)\) is a metric measure space of homogeneous type with a finite measure.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 2083994
zbMATH Keywords: extension operator
zbMATH Keywords: metric spaces of homogeneous type
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: realanalexch.27.2.0583
OpenAlex ID: W1498032066
DOI: 10.14321/REALANALEXCH.27.2.0583
description: scientific article; zbMATH DE number 2083994