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

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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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

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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. È. Shambilova, “Iterated Integral Operators on the Cone of Monotone Functions”, Math. Notes, 104:3 (2018), 443–453
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
3. V. D. Stepanov, G. E. Shambilova, “On iterated and bilinear integral Hardy-type operators”, Math. Inequal. Appl., 22:4 (2019), 1505–1533
4. V. D. Stepanov, G. È. Shambilova, “Bilinear Weighted Inequalities With Volterra Integral Operators”, Dokl. Math., 99:3 (2019), 290–294
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