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 Tr. Mat. Inst. Steklova, 2016, Volume 293, Pages 113–132 (Mi tm3708)

An analog of Young's inequality for convolutions of functions for general Morrey-type spaces

V. I. Burenkova, T. V. Tararykovab

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b School of Mathematics, Cardiff University, Senghennydd Road, CF24 4AG Cardiff, Wales, UK

Abstract: An analog of the classical Young's inequality for convolutions of functions is proved in the case of general global Morrey-type spaces. The form of this analog is different from Young's inequality for convolutions in the case of Lebesgue spaces. A separate analysis is performed for the case of periodic functions.

 Funding Agency Grant Number Russian Science Foundation 14-11-00443 The work of V. I. Burenkov (Sections 1–4) is supported by the Russian Science Foundation under grant 14-11-00443 and performed in Steklov Mathematical Institute of Russian Academy of Sciences. Section 5 is written by T. V. Tararykova.

DOI: https://doi.org/10.1134/S0371968516020084

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 293, 107–126

Bibliographic databases:

UDC: 517.518

Citation: V. I. Burenkov, T. V. Tararykova, “An analog of Young's inequality for convolutions of functions for general Morrey-type spaces”, 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, 113–132; Proc. Steklov Inst. Math., 293 (2016), 107–126

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3708
• https://doi.org/10.1134/S0371968516020084
• http://mi.mathnet.ru/eng/tm/v293/p113

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This publication is cited in the following articles:
1. O. G. Avsyankin, “On the Compactness of Convolution-Type Operators in Morrey Spaces”, Math. Notes, 102:4 (2017), 437–443
2. N. A. Bokayev, V. I. Burenkov, D. T. Matin, “On precompactness of a set in general local and global Morrey-type spaces”, Eurasian Math. J., 8:3 (2017), 109–115
3. A. Almeida, S. Samko, “Approximation in generalized Morrey spaces”, Georgian Math. J., 25:2 (2018), 155–168
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. O. G. Avsyankin, “Compactness of Some Operators of Convolution Type in Generalized Morrey Spaces”, Math. Notes, 104:3 (2018), 331–338
6. F. A. Guliyeva, S. R. Sadigova, “On some properties of convolution in Morrey type spaces”, Azerb. J. Math., 8:1 (2018), 140–150
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