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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
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
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
Linking options:
https://www.mathnet.ru/eng/tm3519https://doi.org/10.1134/S0371968514010063 https://www.mathnet.ru/eng/tm/v284/p105
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