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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 2, Pages 452–465 (Mi smj1081)  

This article is cited in 5 scientific papers (total in 5 papers)

Embedding theorems for a certain function class of Sobolev type on metric spaces

A. S. Romanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (230 kB) Citations (5)
References:
Abstract: Given a metric space with a Borel measure $\mu$, we consider a class of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function $p$-summable with respect to $\mu$. We prove some analogs of the classical theorems on embedding Sobolev function classes into Lebesgue spaces.
Keywords: metric space, measure, Sobolev class, embedding theorem.
Received: 25.06.2003
English version:
Siberian Mathematical Journal, 2004, Volume 45, Issue 2, Pages 376–387
DOI: https://doi.org/10.1023/B:SIMJ.0000021292.79527.b5
Bibliographic databases:
UDC: 517.51
Language: Russian
Citation: A. S. Romanov, “Embedding theorems for a certain function class of Sobolev type on metric spaces”, Sibirsk. Mat. Zh., 45:2 (2004), 452–465; Siberian Math. J., 45:2 (2004), 376–387
Citation in format AMSBIB
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\by A.~S.~Romanov
\paper Embedding theorems for a~certain function class of Sobolev type on metric spaces
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
\issue 2
\pages 452--465
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\zmath{https://zbmath.org/?q=an:1058.46016}
\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 2
\pages 376--387
\crossref{https://doi.org/10.1023/B:SIMJ.0000021292.79527.b5}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000220959600016}
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  • https://www.mathnet.ru/eng/smj/v45/i2/p452
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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