D. V. Prokhorov, V. D. Stepanov, “On weighted Hardy inequalities in mixed norms”, Function theory and equations of mathematical physics, Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth, Trudy Mat. Inst. Steklova, 283, MAIK Nauka/Interperiodica, Moscow, 2013, 155–170; Proc. Steklov Inst. Math., 283 (2013), 149

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 283, Pages 155–170
DOI: https://doi.org/10.1134/S0371968513040110 (Mi tm3513)

This article is cited in 30 scientific papers (total in 30 papers)

On weighted Hardy inequalities in mixed norms

D. V. Prokhorov^a, V. D. Stepanov^b

^a Computer Centre Far-Eastern Branch of RAS, Khabarovsk, Russia
^b Peoples Friendship University of Russia, Moscow, Russia

Full-text PDF (232 kB) Citations (30)

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DOI: https://doi.org/10.1134/S0371968513040110

Abstract: A characterization of weighted Hardy inequalities in mixed norms on a half-axis is obtained.

Received in September 2012

English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 283, Pages 149–164
DOI: https://doi.org/10.1134/S0081543813080117

Bibliographic databases:

Document Type: Article

UDC: 517.51

Language: Russian

Citation: D. V. Prokhorov, V. D. Stepanov, “On weighted Hardy inequalities in mixed norms”, Function theory and equations of mathematical physics, Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth, Trudy Mat. Inst. Steklova, 283, MAIK Nauka/Interperiodica, Moscow, 2013, 155–170; Proc. Steklov Inst. Math., 283 (2013), 149–164

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tm3513

https://doi.org/10.1134/S0371968513040110

https://www.mathnet.ru/eng/tm/v283/p155

This publication is cited in the following 30 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
Amiran Gogatishvili, Tuğçe Ünver, “New characterization of weighted inequalities involving superposition of Hardy integral operators”, Mathematische Nachrichten, 2024
Aigerim Kalybay, “Hardy-type inequalities for a class of iterated operators and their application to Morrey-type spaces”, Open Mathematics, 22:1 (2024)
N. Zhangabergenova, A. Temirkhanova, “Iterated discrete Hardy-type inequalities”, Eurasian Math. J., 14:1 (2023), 81–95
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
Krepela M. Pick L., “Weighted Inequalities For Iterated Copson Integral Operators”, Studia Math., 253:2 (2020), 163–197
Bilgicli N. Mustafayev R.Ch. Unver T., “Multidimensional Bilinear Hardy Inequalities”, Azerbaijan J. Math., 10:1 (2020), 127–161
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
Stepanov V.D. Shambilova G.E., “On Iterated and Bilinear Integral Hardy-Type Operators”, Math. Inequal. Appl., 22:4 (2019), 1505–1533
R. Mustafayev, “On weighted iterated Hardy-type inequalities”, Positivity, 22:1 (2018), 275–299
V. D. Stepanov, G. E. Shambilova, “On weighted iterated Hardy-type operators”, Anal. Math., 44:2 (2018), 273–283
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
I. K. Shafigullin, “Lower bound for the Hardy constant for an arbitrary domain in $\mathbb{R}^n$ ”, Ufa Math. J., 9:2 (2017), 102–108
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
V. D. Stepanov, G. E. Shambilova, “On bilinear weighted inequalities on the cone of nondecreasing functions”, Dokl. Math., 96:3 (2017), 631–635
A. Gogatishvili, R. Ch. Mustafayev, “Iterated Hardy-type inequalities involving suprema”, Math. Inequal. Appl., 20:4 (2017), 901–927
A. Gogatishvili, R. Ch. Mustafayev, “Weighted iterated Hardy-type inequalities”, Math. Inequal. Appl., 20:3 (2017), 683–728
D. V. Prokhorov, “On a class of weighted inequalities containing quasilinear operators”, Proc. Steklov Inst. Math., 293 (2016), 272–287

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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