Lebesgue constants and Hardy–Littlewood theorem for Morrey spaces

Berezhnoi E.I. Nursultanov E.D.
1 January 2026 Academic Press Inc.

Journal of Mathematical Analysis and Applications
2026 #553 Issue 1

Based on a new approach for a class of global Morrey spaces and a class of local Morrey spaces, we give an exact description of the Lebesgue constants. Although a Morrey space depends on three parameters, it is shown that the Lebesgue constant for Morrey spaces depends on only two parameters. Estimates of the Fourier coefficients of functions from Morrey spaces are given that are similar to the Hardy–Littlewood theorem and its refinement by E. Nursultanov.

Fourier series , Global Morrey spaces , Lebesque constant , Local Morrey spaces

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Department of Mathematics, P.G. Demidov Yaroslavl State University, 14, Sovetskaya St, Yaroslavl, 150 000, Russian Federation
Regional Mathematical Center, Southern Federal University, Rostov-on-Don, 344090, Russian Federation
Department of Mathematics, Lomonosov Moscow State University, Kazakh Branch, Astana, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Department of Mathematics
Regional Mathematical Center
Department of Mathematics
Institute of Mathematics and Mathematical Modeling

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