Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings
type: Item
instance of: scholarly article
title: Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings
zbMATH Open document ID: 1322.46025
DOI: 10.1134/S0037446614050048
published in: Siberian Mathematical Journal
publication date: 2015-01-15T00:00:00Z
review text: Let \(D\) and \(D'\) be domains in a Carnot group \(G\) whose Hausdorff dimension is \(\nu\), \(L_p^1(D)\) be the homogeneous Sobolev space on \(D\), \(p\geq 1\), \(p\neq\nu\). In the paper under review, the authors study the properties of a measurable mapping \(\varphi: D\mapsto D'\) for which the superposition operator \(\varphi^*: f\mapsto f\circ\varphi\) is an isomorphism of the homogeneous Sobolev spaces \(L_p^1(D)\) and \(L_p^1(D')\).
reviewed by: Sergei S. Platonov
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 6386964
zbMATH Keywords: superposition operator
zbMATH Keywords: Sobolev space
zbMATH Keywords: quasi-isometry
zbMATH Keywords: Carnot group
author: S. K. Vodop'yanov
author: Nikita Evseev
MaRDI profile type: Publication
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full work available at URL: s0037446614050048
OpenAlex ID: W2056175117
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description: scientific article; zbMATH DE number 6386964