RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Tr. Mat. Inst. Steklova, 2016, Volume 293, Pages 236–262 (Mi tm3717)  

This article is cited in 8 scientific papers (total in 8 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: PDF file (318 kB)
References: PDF file   HTML file

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
\Bibitem{NasUsh16}
\by M.~G.~Nasyrova, E.~P.~Ushakova
\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 Tr. Mat. Inst. Steklova
\yr 2016
\vol 293
\pages 236--262
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3717}
\crossref{https://doi.org/10.1134/S0371968516020175}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3628483}
\elib{http://elibrary.ru/item.asp?id=26344482}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 293
\pages 228--254
\crossref{https://doi.org/10.1134/S0081543816040179}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380722200017}
\elib{http://elibrary.ru/item.asp?id=27120313}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84980012051}


Linking options:
  • http://mi.mathnet.ru/eng/tm3717
  • https://doi.org/10.1134/S0371968516020175
  • http://mi.mathnet.ru/eng/tm/v293/p236

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Integral Operators”, Proc. Steklov Inst. Math., 300, suppl. 2 (2018), 1–112  mathnet  crossref  crossref  zmath  isi  elib
    2. D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “On weighted Sobolev spaces on the real line”, Dokl. Math., 93:1 (2016), 78–81  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    3. 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  crossref  zmath  isi  scopus
    4. E. P. Ushakova, “Alternative boundedness characteristics for the Hardy–Steklov operator”, Eurasian Math. J., 8:2 (2017), 74–96  mathnet  mathscinet
    5. 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  mathnet  mathnet  crossref  crossref  zmath  isi  elib  elib  scopus
    6. 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  mathnet  crossref  crossref  zmath  isi  elib  elib  scopus
    7. P. Jain, S. Kanjilal, V. D. Stepanov, E. P. Ushakova, “On bilinear Hardy–Steklov operators”, Dokl. Math., 98:3 (2018), 634–637  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    8. 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  mathnet  crossref  crossref  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:141
    Full text:8
    References:26
    First page:7

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019