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Sbornik: Mathematics, 2016, Volume 207, Issue 8, Pages 1159–1186
DOI: https://doi.org/10.1070/SM8535 (Mi sm8535) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces

D. V. Prokhorov, V. D. Stepanov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (605 kB) Citations (15) Russian version article
References:
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DOI: https://doi.org/10.1070/SM8535
Abstract: A precise characterization of inequalities in weighted Lebesgue spaces with positive quasilinear integral operators of iterative type on the half-axis is given. All cases of positive integration parameters are treated, including the case of supremum. Applications to the solution of the well-known problem of the boundedness of the Hardy-Littlewood maximal operator in weighted Lorentz $\Gamma$-spaces are given.
Bibliography: 41 titles.
Keywords: integral operator, weighted inequality, Lebesgue space, Lorentz space.
Funding agency Grant number
Russian Science Foundation 14-11-00443
The work is supported by the Russian Science Foundation (grant no. 14-11-00443).
Received: 29.04.2015
Bibliographic databases:
Document Type: Article
UDC: 517.51+517.98
MSC: Primary 26D15; Secondary 47G10
Language: English
Original paper language: Russian
Citation: D. V. Prokhorov, V. D. Stepanov, “Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces”, Sb. Math., 207:8 (2016), 1159–1186
Citation in format AMSBIB
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\pages 1159--1186
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  • https://www.mathnet.ru/eng/sm/v207/i8/p135
    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:586
    Russian version PDF:107
    English version PDF:41
    References:74
    First page:41
     
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