Monotone functions and quasiconformal mappings on Carnot groups
type: Item
instance of: scholarly article
title: Monotone functions and quasiconformal mappings on Carnot groups
zbMATH Open document ID: 0876.30020
DOI: 10.1007/BF02106736
published in: Siberian Mathematical Journal
publication date: 1997-11-20T00:00:00Z
review text: Let \(G\) be a Carnot group with the homogeneous dimension \(\nu\), \(\Omega\) be a domain in \(G\), \(W^1_p (\Omega)\) and \(L^1_p (\Omega)\), \(1\leq p\leq \infty\), be the Sobolev spaces and the class \(W^1_{p,loc} (\Omega)\) consists of all functions \(f\) such that \(f\in W^1_p (U)\) for every open set \(U\), \(\overline U\subset \Omega\). The author investigates monotone functions of the Sobolev classes and obtains the following results: monotone functions of the class \(L^1_\nu\) are continuous and their family with uniformly bounded Dirichlet integrals is equicontinuous; monotone mappings of class \(W^1_{\nu,loc}\) satisfy Luzin's condition \(({\mathcal N})\). A theorem of structure isomorphism between Sobolev spaces on Carnot groups and a theorem on removable singularities of quasiconformal mappings have been established.
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 22E15
zbMATH DE Number: 1023885
zbMATH Keywords: homogeneous group
zbMATH Keywords: Carnot group
zbMATH Keywords: Sobolev spaces
author: S. K. Vodop'yanov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02106736
OpenAlex ID: W37034644
description: scientific article; zbMATH DE number 1023885