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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)
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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
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 8, Pages 135–162
DOI: https://doi.org/10.4213/sm8535
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”, Mat. Sb., 207:8 (2016), 135–162; Sb. Math., 207:8 (2016), 1159–1186
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:33
    References:71
    First page:41
     
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