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Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 989–1029 (Mi smj2693)  

This article is cited in 3 scientific papers (total in 3 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

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.

DOI: https://doi.org/10.17377/smzh.2015.56.503

Full text: PDF file (564 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:5, 789–821

Bibliographic databases:

UDC: 517.518+517.54
Received: 16.02.2015

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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\paper Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. K. Vodopyanov, “On admissible changes of variables for Sobolev functions on (sub)Riemannian manifolds”, Dokl. Math., 93:3 (2016), 318–321  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. S. Romanov, “Operatory kompozitsii v prostranstvakh Soboleva s peremennym pokazatelem summiruemosti”, Sib. elektron. matem. izv., 14 (2017), 794–806  mathnet  crossref
    3. S. K. Vodopyanov, “Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds”, Sb. Math., 210:1 (2019), 59–104  mathnet  crossref  crossref  adsnasa  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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