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.
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
\Bibitem{Sha14}
\by G.~E.~Shambilova
\paper The weighted inequalities for a~certain class of quasilinear integral operators on the cone of monotone functions
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 4
\pages 912--936
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\transl
\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 4
\pages 745--767
\crossref{https://doi.org/10.1134/S0037446614040168}
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Linking options:
https://www.mathnet.ru/eng/smj2581
https://www.mathnet.ru/eng/smj/v55/i4/p912
This publication is cited in the following 12 articles:
V. D. Stepanov, G. E. Shambilova, “On the Iterated Integral Operators on the Cone of Monotone Functions”, Sib Math J, 66:2 (2025), 345
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
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
A. A. Kalybay, “Weighted estimates for a class of quasilinear integral operators”, Siberian Math. J., 60:2 (2019), 291–303
V. D. Stepanov, G. E. Shambilova, “On iterated and bilinear integral Hardy-type operators”, Math. Inequal. Appl., 22:4 (2019), 1505–1533
V. D. Stepanov, G. È. Shambilova, “Iterated Integral Operators on the Cone of Monotone Functions”, Math. Notes, 104:3 (2018), 443–453
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
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
A. Gogatishvili, R. Ch. Mustafayev, “Iterated Hardy-type inequalities involving suprema”, Math. Inequal. Appl., 20:4 (2017), 901–927
V. D. Stepanov, G. È. Shambilova, Dokl. Math., 96:1 (2017), 315–320
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
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
Citation in format AMSBIB
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