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Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings

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Abstract

We study the properties of the mappings on a Carnot group which induce, via the change-of-variables rule, the isomorphisms of Sobolev spaces with the summability exponent different from the Hausdorff dimension of the group.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 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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Correspondence to S. K. Vodop’yanov.

Additional information

Original Russian Text Copyright © 2014 Vodop’yanov S.K. and Evseev N.A.

The authors were partially supported by a Grant of the Government of the Russian Federation (Agreement No. 14.B25.31.0029).

To dear Yuriĭ Grigor’evich Reshetnyak on the occasion of his 85th birthday.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 5, pp. 1001–1039, September–October, 2014.

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Vodop’yanov, S.K., Evseev, N.A. Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings. Sib Math J 55, 817–848 (2014). https://doi.org/10.1134/S0037446614050048

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  • DOI: https://doi.org/10.1134/S0037446614050048

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