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Matematicheskie Zametki, 2009, Volume 86, Issue 6, Pages 829–844
DOI: https://doi.org/10.4213/mzm8526 (Mi mzm8526) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Compactness of Embeddings of Sobolev Type on Metric Measure Spaces

I. A. Ivanishko, V. G. Krotov

Belarusian State University
Full-text PDF (596 kB) Citations (18)
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DOI: https://doi.org/10.4213/mzm8526
Abstract: We establish conditions for the compactness of embeddings for some classes of functions on metric space with measure satisfying the duplication condition. These classes are defined in terms of the $L^p$-summability of maximal functions measuring local smoothness.
Keywords: embedding of Sobolev type, metric measure space, Hardy–Littlewood maximal function, Hölder class, Sobolev space, Borel measure, Lebesgue measure.
Received: 06.04.2009
English version:
Mathematical Notes, 2009, Volume 86, Issue 6, Pages 775–788
DOI: https://doi.org/10.1134/S0001434609110200
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: I. A. Ivanishko, V. G. Krotov, “Compactness of Embeddings of Sobolev Type on Metric Measure Spaces”, Mat. Zametki, 86:6 (2009), 829–844; Math. Notes, 86:6 (2009), 775–788
Citation in format AMSBIB
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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