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Sibirsk. Mat. Zh., 2014, Volume 55, Number 5, Pages 1001–1039 (Mi smj2586)  

This article is cited in 11 scientific papers (total in 11 papers)

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

S. K. Vodop'yanovab, N. A. Evseevab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

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.

Keywords: superposition operator, Sobolev space, quasi-isometry, Carnot group.

Full text: PDF file (549 kB)
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English version:
Siberian Mathematical Journal, 2014, 55:5, 817–848

Bibliographic databases:

UDC: 517.518+517.54
Received: 20.12.2013

Citation: S. K. Vodop'yanov, N. A. Evseev, “Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings”, Sibirsk. Mat. Zh., 55:5 (2014), 1001–1039; Siberian Math. J., 55:5 (2014), 817–848

Citation in format AMSBIB
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\paper Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings
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\vol 55
\issue 5
\pages 1001--1039
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\issue 5
\pages 817--848
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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. Vodop'yanov, N. A. Evseev, “Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings”, Siberian Math. J., 56:5 (2015), 789–821  mathnet  crossref  crossref  isi  elib  elib
    2. N. A. Evseev, “Change of variables operators in weighted Sobolev spaces on Carnot groups”, J. Math. Sci., 221:6 (2017), 826–832  mathnet  crossref  crossref
    3. N. A. Evseev, “Composition operators in weighted Sobolev spaces on the Carnot group”, Siberian Math. J., 56:6 (2015), 1042–1059  mathnet  crossref  crossref  mathscinet  isi  elib
    4. S. K. Vodop'yanov, N. A. Evseev, “Isomorphisms of Sobolev spaces on Carnot groups and metric properties of mappings”, Dokl. Math., 92:2 (2015), 532–536  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    5. Yu. V. Dymchenko, “Equality of the capacity and module of a condenser on a sub-Finsler space”, J. Math. Sci. (N. Y.), 225:6 (2017), 883–892  mathnet  crossref  mathscinet
    6. 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
    7. I. D. Platis, “Quasiconformal mappings on the Heisenberg group: an overview”, Handbook of Teichmueller Theory, v. VI, IRMA Lectures in Mathematics and Theoretical Physics, 27, ed. A. Papadopoulos, European Mathematical Soc., 2016, 375–393  mathscinet  zmath  isi
    8. N. Evseev, “Measurability of the Banach indicatrix”, Colloq. Math., 153:1 (2018), 97–101  crossref  mathscinet  zmath  isi  scopus
    9. 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
    10. S. K. Vodopyanov, “Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings”, Siberian Math. J., 60:5 (2019), 774–804  mathnet  crossref  crossref  isi  elib
    11. S. K. Vodopyanov, “O regulyarnosti otobrazhenii, obratnykh k sobolevskim, i teoriya $\mathscr{Q}_{q,p}$-gomeomorfizmov”, Sib. matem. zhurn., 61:6 (2020), 1257–1299  mathnet  crossref
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