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.
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.
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, Trudy Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 113–132; Proc. Steklov Inst. Math., 293 (2016), 107–126
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\paper An analog of Young's inequality for convolutions of functions for general Morrey-type spaces
\inbook Function spaces, approximation theory, and related problems of mathematical analysis
\bookinfo Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2016
\vol 293
\pages 113--132
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 293
\pages 107--126
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https://doi.org/10.1134/S0371968516020084
https://www.mathnet.ru/eng/tm/v293/p113
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