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Eurasian Math. J., 2017, Volume 8, Number 2, Pages 47–73 (Mi emj256)  

This article is cited in 4 scientific papers (total in 4 papers)

On the boundedness of quasilinear integral operators of iterated type with Oinarov's kernels on the cone of monotone functions

V. D. Stepanovab, G. E. Shambilovac

a Steklov Institute of Mathematics, 8 Gubkina St, 119991 Moscow, Russia
b Department of Nonlinear Analysis and Optimization, RUDN University, 6 Miklukho-Maklay St, 117198 Moscow, Russia
c Department of Mathematics, Financial University under the Government of the Russian Federation, 49 Leningradsky Prospekt, 125993 Moscow, Russia

Abstract: We solve the characterization problem of $L_v^p-L_{\rho}^r$ weighted inequalities on Lebesgue cones of monotone functions on the half-axis for quasilinear integral operators of iterated type with Oinarov's kernels.

Keywords and phrases: Hardy type inequality, weighted Lebesgue space, quasilinear integral operator, Oinarov's kernel, cone of monotone functions.

Funding Agency Grant Number
Russian Science Foundation 16-41-02004
The research work of G.E. Shambilova and V.D. Stepanov was carried out at the Peoples' Friendship University of Russia and Financially supported by the Russian Science Foundation (Project no. 16-41-02004).


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MSC: 26D15
Received: 18.11.2016
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Citation: 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

Citation in format AMSBIB
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\by V.~D.~Stepanov, G.~E.~Shambilova
\paper On the boundedness of quasilinear integral operators of iterated type with Oinarov's kernels on the cone of monotone functions
\jour Eurasian Math. J.
\yr 2017
\vol 8
\issue 2
\pages 47--73
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85029000685}


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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. È. Shambilova, “Iterated Integral Operators on the Cone of Monotone Functions”, Math. Notes, 104:3 (2018), 443–453  mathnet  crossref  crossref  mathscinet  isi  elib
    2. 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
    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, “Bilinear Weighted Inequalities With Volterra Integral Operators”, Dokl. Math., 99:3 (2019), 290–294  mathnet  crossref  zmath  isi  scopus
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