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 Tr. Mat. Inst. Steklova, 2014, Volume 284, Pages 105–137 (Mi tm3519)

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

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

Bibliographic databases:

UDC: 517.518

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

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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
2. E. I. Berezhnoi, “A discrete version of local Morrey spaces”, Izv. Math., 81:1 (2017), 1–28
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
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
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
6. D. I. Hakim, “Complex interpolation of predual spaces of general local Morrey-type spaces”, Banach J. Math. Anal., 12:3 (2018), 541–571
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
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