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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 5, Pages 989–1029
DOI: https://doi.org/10.17377/smzh.2015.56.503 (Mi smj2693) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings

S. K. Vodop'yanovab, N. A. Evseevba

a Novosibirsk State University, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Full-text PDF (564 kB) Citations (7)
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DOI: https://doi.org/10.17377/smzh.2015.56.503
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.
Received: 16.02.2015
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 5, Pages 789–821
DOI: https://doi.org/10.1134/S0037446615050031
Bibliographic databases:
Document Type: Article
UDC: 517.518+517.54
Language: Russian
Citation: S. K. Vodop'yanov, N. A. Evseev, “Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings”, Sibirsk. Mat. Zh., 56:5 (2015), 989–1029; Siberian Math. J., 56:5 (2015), 789–821
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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