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Siberian Mathematical Journal

, Volume 56, Issue 5, pp 789–821 | Cite as

Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings

  • S. K. Vodop’yanovEmail author
  • N. A. Evseev
Article

Abstract

We prove that a measurable mapping of domains on a Carnot group induces by the corresponding change of variables an isomorphism of the Sobolev spaces whose integrability exponent is equal to the Hausdorff dimension of the group if and only if the mapping coincides with a quasiconformal mapping almost everywhere.

Keywords

composition operator Sobolev space quasiconformal mapping Carnot group 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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