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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 284, Pages 105–137
DOI: https://doi.org/10.1134/S0371968514010063
(Mi tm3519)
 

This article is cited in 24 scientific papers (total in 24 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
References:
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.
Received in April 2013
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 284, Pages 97–128
DOI: https://doi.org/10.1134/S0081543814010064
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
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, Trudy Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 105–137; Proc. Steklov Inst. Math., 284 (2014), 97–128
Citation in format AMSBIB
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\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 Trudy Mat. Inst. Steklova
\yr 2014
\vol 284
\pages 105--137
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • This publication is cited in the following 24 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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