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Tr. Mat. Inst. Steklova, 2016, Volume 293, Pages 236–262
(Mi tm3717)
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This article is cited in 9 scientific papers (total in 9 papers)
Hardy–Steklov operators and Sobolev-type embedding inequalities
M. G. Nasyrovaa, E. P. Ushakovab
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
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. |
DOI:
https://doi.org/10.1134/S0371968516020175
 Full text:
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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 293, 228–254
Bibliographic databases:
   
UDC:
517.51
Received: November 10, 2015
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, Tr. Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 236–262; Proc. Steklov Inst. Math., 293 (2016), 228–254
Citation in format AMSBIB
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\serial Tr. Mat. Inst. Steklova
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\vol 293
\pages 236--262
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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Linking options:
http://mi.mathnet.ru/eng/tm3717https://doi.org/10.1134/S0371968516020175 http://mi.mathnet.ru/eng/tm/v293/p236
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This publication is cited in the following articles:
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D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Integral Operators”, Proc. Steklov Inst. Math., 300, suppl. 2 (2018), 1–112
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D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “On weighted Sobolev spaces on the real line”, Dokl. Math., 93:1 (2016), 78–81
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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
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E. P. Ushakova, “Alternative boundedness characteristics for the Hardy–Steklov operator”, Eurasian Math. J., 8:2 (2017), 74–96
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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
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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
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P. Jain, S. Kanjilal, V. D. Stepanov, E. P. Ushakova, “On bilinear Hardy–Steklov operators”, Dokl. Math., 98:3 (2018), 634–637
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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
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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
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