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Sibirsk. Mat. Zh., 2015, Volume 56, Number 6, Pages 1304–1325 (Mi smj2714)  

This article is cited in 2 scientific papers (total in 2 papers)

Composition operators in weighted Sobolev spaces on the Carnot group

N. A. Evseevab

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

Abstract: We study the properties of the mappings inducing bounded change-of-variable operators in weighted Sobolev spaces on the Carnot group. We obtain an analytical description of these mappings in terms of integrability of the weighted distortion function. In some cases we prove that the mapping inducing a bounded operator is piecewise absolutely continuous on almost all horizontal lines.

Keywords: composition operator, weighted Sobolev space, Carnot group.

DOI: https://doi.org/10.17377/smzh.2015.56.608

Full text: PDF file (392 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:6, 1042–1059

Bibliographic databases:

UDC: 517.518+517.54
Received: 02.07.2015

Citation: N. A. Evseev, “Composition operators in weighted Sobolev spaces on the Carnot group”, Sibirsk. Mat. Zh., 56:6 (2015), 1304–1325; Siberian Math. J., 56:6 (2015), 1042–1059

Citation in format AMSBIB
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\by N.~A.~Evseev
\paper Composition operators in weighted Sobolev spaces on the Carnot group
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 6
\pages 1304--1325
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\crossref{https://doi.org/10.17377/smzh.2015.56.608}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3492907}
\elib{https://elibrary.ru/item.asp?id=24817521}
\transl
\jour Siberian Math. J.
\yr 2015
\vol 56
\issue 6
\pages 1042--1059
\crossref{https://doi.org/10.1134/S0037446615060087}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84952940426}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. Evseev, “Measurability of the Banach indicatrix”, Colloq. Math., 153:1 (2018), 97–101  crossref  mathscinet  zmath  isi  scopus
    2. N. A. Evseev, A. V. Menovshchikov, “The Composition Operator on Mixed-Norm Lebesgue Spaces”, Math. Notes, 105:6 (2019), 812–817  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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