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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. 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
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
Citation in format AMSBIB
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\paper Hardy--Steklov operators and Sobolev-type embedding inequalities
\inbook Function spaces, approximation theory, and related problems of mathematical analysis
\bookinfo Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2016
\vol 293
\pages 236--262
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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