Sobolev spaces and \((P,Q)\)-quasiconformal mappings of Carnot groups
type: Item
instance of: scholarly article
title: Sobolev spaces and \((P,Q)\)-quasiconformal mappings of Carnot groups
zbMATH Open document ID: 0917.46023
DOI: 10.1007/BF02673052
published in: Siberian Mathematical Journal
publication date: 1999-05-10T00:00:00Z
review text: Measurable functions \(\varphi \: G\to G'\) are considered which induce an isomorphism \(\varphi^*\) between the Sobolev spaces \(L^1_n(G)\) and \(L^1_n(G')\) by the rule \(\varphi^*(f)=f\circ \varphi\), \(f\in L^1_n\). Here \(G\subset \mathbb R^n\), \(G'\subset \mathbb R^n\), and the Sobolev spaces \(L^1_n(G)\), \(L^1_n(G')\) are equipped with the Carnot--Carathéodory metric. Metric and analytic properties are also studied of mappings which induce bounded embedding operators \(\varphi^* \:L^1_p(G) \to L^1_q(G')\), \(1\leq q\leq p<\infty\).
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 1285466
zbMATH Keywords: capacity
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: Carnot-Carathéodory metric
zbMATH Keywords: bounded embedding operators
author: S. K. Vodop'yanov
author: A. Ukhlov
MaRDI profile type: Publication
cites work: Algebraic Criterion on Quasiconformal Equivalence of Riemann Surfaces
cites work: Quasiconformal Mappings and Royden Algebras in Space
cites work: Asymptotic behavior of solutions of a nonlinear diffusion equation with a source term of general form
cites work: A change of variable that preserves the differential properties of functions
cites work: Q3996375
cites work: Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
cites work: Homeomorphisms that induce monomorphisms of Sobolev spaces
cites work: On mappings generating the embeddings of Sobolev spaces
cites work: Applications of change of variables operators for exact embedding theorems
cites work: Strong Rigidity of Locally Symmetric Spaces. (AM-78)
cites work: Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
cites work: Foundations for the theory of quasiconformal mappings on the Heisenberg group
cites work: Analytic properties of quasiconformal mappings on Carnot groups
cites work: Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
cites work: Q5607484
cites work: Subelliptic estimates and function spaces on nilpotent Lie groups
Wikidata QID: Q126227058
description: scientific article; zbMATH DE number 1285466