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Sibirsk. Mat. Zh., 2014, Volume 55, Number 4, Pages 912–936 (Mi smj2581)  

This article is cited in 11 scientific papers (total in 11 papers)

The weighted inequalities for a certain class of quasilinear integral operators on the cone of monotone functions

G. E. Shambilova

Peoples' Friendship University of Russia, Moscow, Russia

Abstract: We study the problem of characterizing the weighted inequalities on the Lebesgue cones of monotone functions on the semiaxis for a class of quasilinear integral operators.

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

Full text: PDF file (371 kB)
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English version:
Siberian Mathematical Journal, 2014, 55:4, 745–767

Bibliographic databases:

UDC: 517.51
Received: 30.09.2013

Citation: G. E. Shambilova, “The weighted inequalities for a certain class of quasilinear integral operators on the cone of monotone functions”, Sibirsk. Mat. Zh., 55:4 (2014), 912–936; Siberian Math. J., 55:4 (2014), 745–767

Citation in format AMSBIB
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\vol 55
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\pages 912--936
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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, “Boundedness of quasilinear integral operators on the cone of monotone functions”, Siberian Math. J., 57:5 (2016), 884–904  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. V. D. Stepanov, G. È. Shambilova, “Boundedness of a class of quasilinear operators on the cone of monotone functions”, Dokl. Math., 94:3 (2016), 697–702  mathnet  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. 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
    4. A. Gogatishvili, R. Ch. Mustafayev, “Iterated Hardy-type inequalities involving suprema”, Math. Inequal. Appl., 20:4 (2017), 901–927  crossref  mathscinet  zmath  isi  scopus
    5. V. D. Stepanov, G. È. Shambilova, Dokl. Math., 96:1 (2017), 315–320  mathnet  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    6. 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
    7. 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
    8. 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  mathscinet  adsnasa  isi  elib
    9. 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
    10. 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
    11. Mustafayev R., Bilgicli N., “Boundedness of Weighted Iterated Hardy-Type Operators Involving Suprema From Weighted Lebesgue Spaces Into Weighted Cesaro Function Spaces”, Real Anal. Exch., 45:2 (2020), 339–374  crossref  mathscinet  zmath  isi
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