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Mat. Sb., 2016, Volume 207, Number 8, Pages 135–162 (Mi msb8535)  

This article is cited in 12 scientific papers (total in 12 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

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).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8535

Full text: PDF file (631 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2016, 207:8, 1159–1186

Bibliographic databases:

UDC: 517.51+517.98
MSC: Primary 26D15; Secondary 47G10
Received: 29.04.2015

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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L.-E. Persson, G. E. Shambilova, V. D. Stepanov, “Weighted Hardy type inequalities for supremum operators on the cones of monotone functions”, J. Inequal. Appl., 2016, 237, 18 pp.  crossref  mathscinet  zmath  isi  scopus
    2. V. D. Stepanov, G. E. Shambilova, “Boundedness of a class of quasilinear operators on the cone of monotone functions”, Dokl. Math., 94:3 (2016), 697–702  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    3. D. V. Prokhorov, “On a class of weighted inequalities containing quasilinear operators”, Proc. Steklov Inst. Math., 293 (2016), 272–287  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. V. D. Stepanov, G. E. Shambilova, “Boundedness of quasilinear integral operators of iterated type with Oinarov’s kernel on the cone of monotone functions”, Dokl. Math., 96:1 (2017), 315–320  mathnet  crossref  crossref  zmath  isi  elib  scopus
    5. V. D. Stepanov, G. E. Shambilova, “On the boundedness of quasilinear integral operators of iterated type with Oinarov's kernels on the cone of monotone functions”, Eurasian Math. J., 8:2 (2017), 47–73  mathnet  mathscinet
    6. V. D. Stepanov, G. E. Shambilova, “On bilinear weighted inequalities on the cone of nondecreasing functions”, Dokl. Math., 96:3 (2017), 631–635  mathnet  crossref  mathscinet  zmath  zmath  isi  elib  scopus
    7. V. D. Stepanov, G. E. Shambilova, “On weighted iterated Hardy-type operators”, Anal. Math., 44:2 (2018), 273–283  crossref  mathscinet  zmath  isi  scopus
    8. V. D. Stepanov, G. È. Shambilova, “Iterated Integral Operators on the Cone of Monotone Functions”, Math. Notes, 104:3 (2018), 443–453  mathnet  crossref  crossref  mathscinet  isi  elib
    9. V. D. Stepanov, G. E. Shambilova, “Reduction of weighted bilinear inequalities with integration operators on the cone of nondecreasing functions”, Siberian Math. J., 59:3 (2018), 505–522  mathnet  crossref  crossref  mathscinet  isi  elib
    10. A. A. Kalybay, R. Oinarov, “Bounds for a class of quasilinear integral operators on the set of non-negative and non-negative monotone functions”, Izv. Math., 83:2 (2019), 251–272  mathnet  crossref  crossref  adsnasa  isi  elib
    11. A. A. Kalybay, “Weighted estimates for a class of quasilinear integral operators”, Siberian Math. J., 60:2 (2019), 291–303  mathnet  crossref  crossref  isi  elib
    12. Stepanov V.D., Shambilova G.E., “On Iterated and Bilinear Integral Hardy-Type Operators”, Math. Inequal. Appl., 22:4 (2019), 1505–1533  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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