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, 2014, Volume 284, Pages 105–137 (Mi tm3519)  

This article is cited in 7 scientific papers (total in 7 papers)

Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations

V. I. Burenkovab, E. D. Nursultanovc, D. K. Chigambayevaa

a Gumilev Eurasian National University, Astana, Kazakhstan
b School of Mathematics, Cardiff University, Cardiff, Wales, UK
c Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan

Abstract: The real interpolation method is considered and it is proved that for general local Morrey-type spaces, in the case in which they have the same integrability parameter, the interpolation spaces are again general local Morrey-type spaces with appropriately chosen parameters. This result is a particular case of the interpolation theorem for much more general spaces defined with the help of an operator acting from some function space to the cone of nonnegative nondecreasing functions on $(0,\infty)$. It is also shown how the classical interpolation theorems due to Stein–Weiss, Peetre, Calderón, Gilbert, Lizorkin, Freitag and some of their new variants can be derived from this theorem.

DOI: https://doi.org/10.1134/S0371968514010063

Full text: PDF file (401 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 284, 97–128

Bibliographic databases:

UDC: 517.518
Received in April 2013

Citation: V. I. Burenkov, E. D. Nursultanov, D. K. Chigambayeva, “Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 105–137; Proc. Steklov Inst. Math., 284 (2014), 97–128

Citation in format AMSBIB
\Bibitem{BurNurChi14}
\by V.~I.~Burenkov, E.~D.~Nursultanov, D.~K.~Chigambayeva
\paper Description of the interpolation spaces for a~pair of local Morrey-type spaces and their generalizations
\inbook Function spaces and related problems of analysis
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 284
\pages 105--137
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3519}
\crossref{https://doi.org/10.1134/S0371968514010063}
\elib{http://elibrary.ru/item.asp?id=21249104}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2014
\vol 284
\pages 97--128
\crossref{https://doi.org/10.1134/S0081543814010064}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000335559000005}
\elib{http://elibrary.ru/item.asp?id=21876691}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899839004}


Linking options:
  • http://mi.mathnet.ru/eng/tm3519
  • https://doi.org/10.1134/S0371968514010063
  • http://mi.mathnet.ru/eng/tm/v284/p105

    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. V. I. Burenkov, T. V. Tararykova, “An analog of Young's inequality for convolutions of functions for general Morrey-type spaces”, Proc. Steklov Inst. Math., 293 (2016), 107–126  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. E. I. Berezhnoi, “A discrete version of local Morrey spaces”, Izv. Math., 81:1 (2017), 1–28  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. Gogatishvili, R. Mustafayev, T. Ünver, “Embedding relations between weighted complementary local Morrey-type spaces and weighted local Morrey-type spaces”, Eurasian Math. J., 8:1 (2017), 34–49  mathnet
    4. V. I. Burenkov, D. K. Chigambayeva, E. D. Nursultanov, “Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces”, Eurasian Math. J., 9:2 (2018), 82–88  mathnet  isi
    5. Y. Sawano, H. Yoshida, “A predual of a predual of $B_{\sigma}$ and its applications to commutators”, Sci. China-Math., 61:8 (2018), 1437–1472  crossref  mathscinet  isi  scopus
    6. D. I. Hakim, “Complex interpolation of predual spaces of general local Morrey-type spaces”, Banach J. Math. Anal., 12:3 (2018), 541–571  crossref  mathscinet  isi
    7. M. Ruzhansky, D. Suragan, N. Yessirkegenov, “Hardy–Littlewood, Bessel–Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces”, Fract. Calc. Appl. Anal., 21:3 (2018), 577–612  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:306
    Full text:26
    References:60

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