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Sbornik: Mathematics, 2012, Volume 203, Issue 7, Pages 1045–1064
DOI: https://doi.org/10.1070/SM2012v203n07ABEH004253 (Mi sm7828) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Criteria for compactness in $L^p$-spaces, $p\geqslant0$

V. G. Krotov

Belarusian State University
English version PDF (415 kB) Citations (18)
References:
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DOI: https://doi.org/10.1070/SM2012v203n07ABEH004253
Abstract: The paper puts forward new compactness criteria for spaces of summable and measurable functions on a metric space with measure satisfying the doubling condition. These criteria are formulated in terms of either local smoothness inequalities or maximal operators that measure local smoothness.
Bibliography: 28 titles.
Keywords: compactness, total boundedness, space of summable functions, space of measurable functions, maximal operators, local smoothness.
Received: 11.12.2010 and 09.09.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 7, Pages 129–148
DOI: https://doi.org/10.4213/sm7828
Bibliographic databases:
Document Type: Article
UDC: 517.518.22
MSC: 46B50, 46E30
Language: English
Original paper language: Russian
Citation: V. G. Krotov, “Criteria for compactness in $L^p$-spaces, $p\geqslant0$”, Mat. Sb., 203:7 (2012), 129–148; Sb. Math., 203:7 (2012), 1045–1064
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2012v203n07ABEH004253
  • https://www.mathnet.ru/eng/sm/v203/i7/p129
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:1377
    Russian version PDF:1436
    English version PDF:81
    References:106
    First page:81
     
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