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Sibirsk. Mat. Zh., 2018, Volume 59, Number 3, Pages 639–658 (Mi smj3000)  

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

Reduction of weighted bilinear inequalities with integration operators on the cone of nondecreasing functions

V. D. Stepanova, G. E. Shambilovab

a Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
b Peoples' Friendship University of Russia, Moscow, Russia

Abstract: We present the reduction methods for characterizing bilinear weighted inequalities on the Lebesgue cones of nondecreasing functions on a half-axis with integration operators.

Keywords: weighted Lebesgue space, quasilinear integral operator, cone of monotone functions.

Funding Agency Grant Number
Russian Science Foundation 16-41-02004
14-11-00443
The results of Section 2 were supported by the Russian Science Foundation (Grant 16-41-02004) and carried out at Peoples' Friendship University of Russia. The results of Section 3 were supported by the Russian Science Foundation under Grant 14-11-00443 and performed in the Steklov Mathematical Institute of the Russian Academy of Sciences.


DOI: https://doi.org/10.17377/smzh.2018.59.313

Full text: PDF file (368 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:3, 505–522

Bibliographic databases:

UDC: 517.51
MSC: 35R30
Received: 22.08.2017

Citation: V. D. Stepanov, G. E. Shambilova, “Reduction of weighted bilinear inequalities with integration operators on the cone of nondecreasing functions”, Sibirsk. Mat. Zh., 59:3 (2018), 639–658; Siberian Math. J., 59:3 (2018), 505–522

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. Jain P., Kanjilal S., Stepanov V.D., Ushakova E.P., “On Bilinear Hardy-Steklov Operators”, Dokl. Math., 98:3 (2018), 634–637  mathnet  crossref  mathscinet  zmath  isi  scopus
    2. V. D. Stepanov, P. Jain, G. È. Shambilova, “Discrete Bilinear Hardy Inequalities”, Dokl. Math., 100:3 (2019), 554–557  mathnet  mathnet  crossref  crossref  zmath  isi  elib  scopus
    3. 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
    4. V. D. Stepanov, G. È. Shambilova, “Multidimensional Bilinear Hardy Inequalities”, Dokl. Math., 100:1 (2019), 374–376  mathnet  mathnet  crossref  crossref  zmath  isi  elib  scopus
    5. 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
    6. V. D. Stepanov, G. E. Shambilova, “Mnogomernye bilineinye neravenstva Khardi”, Sib. matem. zhurn., 61:4 (2020), 913–931  mathnet  crossref
    7. V. D. Stepanov, G. E. Shambilova, “On Two-Dimensional Bilinear Inequalities with Rectangular Hardy Operators in Weighted Lebesgue Spaces”, Proc. Steklov Inst. Math., 312 (2021), 241–248  mathnet  crossref  crossref  isi  elib
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