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Trudy Mat. Inst. Steklova, 2016, Volume 293, Pages 280–295 (Mi tm3719)  

This article is cited in 20 scientific papers (total in 20 papers)

On a class of weighted inequalities containing quasilinear operators

D. V. Prokhorov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: A characterization of weighted $L^p$$L^r$ inequalities on a half-axis is obtained for positive quasilinear operators with Oinarov kernels.

Funding Agency Grant Number
Russian Science Foundation 14-11-00443
This work is supported by the Russian Science Foundation under grant 14-11-00443.


DOI: https://doi.org/10.1134/S0371968516020199

Full text: PDF file (236 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 293, 272–287

Bibliographic databases:

UDC: 517.51
Received: September 17, 2015

Citation: D. V. Prokhorov, “On a class of weighted inequalities containing quasilinear operators”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 280–295; Proc. Steklov Inst. Math., 293 (2016), 272–287

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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. 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. Stepanov V.D., Shambilova G.E., “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. 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. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    5. V. D. Stepanov, G. E. Shambilova, “On weighted iterated Hardy-type operators”, Anal. Math., 44:2 (2018), 273–283  crossref  mathscinet  zmath  isi  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. P. Jain, S. Kanjilal, V. D. Stepanov, E. P. Ushakova, “On bilinear Hardy–Steklov operators”, Dokl. Math., 98:3 (2018), 634–637  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    9. 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
    10. 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
    11. V. D. Stepanov, P. Jain, G. È. Shambilova, “Discrete Bilinear Hardy Inequalities”, Dokl. Math., 100:3 (2019), 554–557  mathnet  crossref  zmath  isi
    12. V. D. Stepanov, G. È. Shambilova, “Bilinear Weighted Inequalities With Volterra Integral Operators”, Dokl. Math., 99:3 (2019), 290–294  mathnet  crossref  zmath  isi
    13. V. D. Stepanov, G. È. Shambilova, “Multidimensional Bilinear Hardy Inequalities”, Dokl. Math., 100:1 (2019), 374–376  mathnet  crossref  zmath  isi
    14. 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
    15. P. Jain, S. Kanjilal, L.-E. Persson, “Hardy-type inequalities over balls in R-N for some bilinear and iterated operators”, J. Inequal. Spec. Funct., 10:2 (2019), 35–48  mathscinet  isi
    16. V. D. Stepanov, G. E. Shambilova, “Mnogomernye bilineinye neravenstva Khardi”, Sib. matem. zhurn., 61:4 (2020), 913–931  mathnet  crossref
    17. M. Krepela, L. Pick, “Weighted inequalities for iterated copson integral operators”, Studia Math., 253:2 (2020), 163–197  crossref  mathscinet  zmath  isi
    18. N. Bilgicli, R. Ch. Mustafayev, T. Unver, “Multidimensional bilinear Hardy inequalities”, Azerbaijan J. Math., 10:1 (2020), 127–161  mathscinet  zmath  isi
    19. V. D. Stepanov, G. E. Shambilova, “Bilinear weighted inequalities with two-dimensional operators”, Dokl. Math., 102:2 (2020), 406–408  crossref  isi
    20. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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