M. G. Nasyrova, E. P. Ushakova, “Hardy–Steklov operators and Sobolev-type embedding inequalities”, 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, 236–262; Proc. Steklov Inst. Math., 293 (2016), 228

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 293, Pages 236–262
DOI: https://doi.org/10.1134/S0371968516020175 (Mi tm3717)

This article is cited in 12 scientific papers (total in 12 papers)

Hardy–Steklov operators and Sobolev-type embedding inequalities

M. G. Nasyrova^a, E. P. Ushakova^b

^a Computing Center, Far Eastern Branch of the Russian Academy of Sciences, ul. Kim Yu Chena 65, Khabarovsk, 680000 Russia
^b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Full-text PDF (318 kB) Citations (12)

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DOI: https://doi.org/10.1134/S0371968516020175

Abstract: We characterize weighted inequalities corresponding to the embedding of a class of absolutely continuous functions into a fractional-order Sobolev space. As auxiliary results of the paper, which are also of independent interest, we obtain several new types of necessary and sufficient conditions for the boundedness of the Hardy–Steklov operator (integral operator with two variable limits) in weighted Lebesgue spaces.

Funding agency	Grant number
Russian Science Foundation	14-11-00443
The work of E. P. Ushakova (Sections 1 and 2) is supported by the Russian Science Foundation under grant 14-11-00443 and performed in Steklov Mathematical Institute of Russian Academy of Sciences. Section 3 is written by M. G. Nasyrova.

Received: November 10, 2015

English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 293, Pages 228–254
DOI: https://doi.org/10.1134/S0081543816040179

Bibliographic databases:

Document Type: Article

UDC: 517.51

Language: Russian

Citation: M. G. Nasyrova, E. P. Ushakova, “Hardy–Steklov operators and Sobolev-type embedding inequalities”, 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, 236–262; Proc. Steklov Inst. Math., 293 (2016), 228–254

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Linking options:

https://www.mathnet.ru/eng/tm3717

https://doi.org/10.1134/S0371968516020175

https://www.mathnet.ru/eng/tm/v293/p236

This publication is cited in the following 12 articles:

W. Albalawi, Z. A. Khan, “Synchronization analysis of multiple integral inequalities driven by Steklov operator”, Fractal Fract., 5:3 (2021), 97 $https://doi.org/10.3390/fractalfract5030097$
V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis”, Math. Notes, 105:1 (2019), 91–103
D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line”, Russian Math. Surveys, 74:6 (2019), 1075–1115
V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov operators and duality principle in weighted Sobolev spaces of the first order”, Dokl. Math., 97:3 (2018), 232–235
D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Spaces associated with weighted Sobolev spaces on the real line”, Dokl. Math., 98:1 (2018), 373–376
P. Jain, S. Kanjilal, V. D. Stepanov, E. P. Ushakova, “On bilinear Hardy–Steklov operators”, Dokl. Math., 98:3 (2018), 634–637
P. Jain, S. Kanjilal, V. D. Stepanov, E. P. Ushakova, “Bilinear Hardy–Steklov Operators”, Math. Notes, 104:6 (2018), 823–832
D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “On associate spaces of weighted Sobolev space on the real line”, Math. Nachr., 290:5-6 (2017), 890–912
E. P. Ushakova, “Alternative boundedness characteristics for the Hardy–Steklov operator”, Eurasian Math. J., 8:2 (2017), 74–96
D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Integral Operators. Part I”, Proc. Steklov Inst. Math., 300, suppl. 2 (2018), 1–112
D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “On weighted Sobolev spaces on the real line”, Dokl. Math., 93:1 (2016), 78–81
D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Integral Operators. Part II”, Proc. Steklov Inst. Math., 302, suppl. 1 (2018), 1–61

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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