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Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings

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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.

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    S. K. Vodop’yanov & N. A. Evseev

  2. Novosibirsk State University, Novosibirsk, Russia

    S. K. Vodop’yanov & N. A. Evseev

Authors
  1. S. K. Vodop’yanov
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  2. N. A. Evseev
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Corresponding author

Correspondence to S. K. Vodop’yanov.

Additional information

Original Russian Text Copyright © 2015 Vodop’yanov S.K. and Evseev N.A.

The authors were partially supported by the Government of the Russian Federation (Grant 14.B25.31.0029) and the Russian Foundation for Basic Research (Grant 14–01–00552).

To S. S. Kutateladze on the occasion of his 70th birthday.

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 5, pp. 989–1029, September–October, 2015; DOI: 10.17377/smzh.2015.56.503.

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Vodop’yanov, S.K., Evseev, N.A. Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings. Sib Math J 56, 789–821 (2015). https://doi.org/10.1134/S0037446615050031

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  • DOI: https://doi.org/10.1134/S0037446615050031

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