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Sibirsk. Mat. Zh., 2016, Volume 57, Number 5, Pages 1131–1155 (Mi smj2779)  

This article is cited in 7 scientific papers (total in 7 papers)

Boundedness of quasilinear integral operators on the cone of monotone functions

V. D. Stepanovab, G. E. Shambilovac

a Peoples' Friendship University of Russia, Moscow, Russia
b Steklov Institute of Mathematics, Moscow, Russia
c Financial University Under the Government of the Russian Federation, Moscow, Russia

Abstract: We study the problem of characterizing weighted inequalities on Lebesgue cones of monotone functions on the half-axis for one class of quasilinear integral operators.

Keywords: Hardy inequality, weighted Lebesgue space, quasilinear integral operator.

Funding Agency Grant Number
Russian Science Foundation 16-41-02004
This research was carried out at the Peoples’ Friendship University of Russia and financially supported by the Russian Science Foundation (Grant 16-41-02004).


DOI: https://doi.org/10.17377/smzh.2016.57.519

Full text: PDF file (375 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2016, 57:5, 884–904

Bibliographic databases:

UDC: 517.51
Received: 16.02.2016
Revised: 16.06.2016

Citation: V. D. Stepanov, G. E. Shambilova, “Boundedness of quasilinear integral operators on the cone of monotone functions”, Sibirsk. Mat. Zh., 57:5 (2016), 1131–1155; Siberian Math. J., 57:5 (2016), 884–904

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. V. D. Stepanov, G. È. Shambilova, Dokl. Math., 96:1 (2017), 315–320  mathnet  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    3. 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
    4. 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
    5. F. G. Avkhadiev, “One-parameter monotone functionals connected with Stieltjes integrals”, Russian Math. (Iz. VUZ), 63:4 (2019), 1–11  mathnet  crossref  crossref  isi
    6. V. D. Stepanov, G. E. Shambilova, “On iterated and bilinear integral Hardy-type operators”, Math. Inequal. Appl., 22:4 (2019), 1505–1533  crossref  mathscinet  zmath  isi  scopus
    7. V. D. Stepanov, G. È. Shambilova, “Bilinear weighted inequalities with Volterra integral operators”, Dokl. Math., 99:3 (2019), 290–294  mathnet  crossref  crossref  zmath  isi  elib  scopus
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