On a necessary condition for belonging of a function to periodic generalized Nikol’sky-Besov-Morrey space in terms of strong summability of Fourier series

Abstract

This paper is dedicated to the investigation of strong summability in the generalized Morrey spaces. First, we study boundedness of the Hardy-Littlewood maximal function on generalized Morrey spaces. We find a necessary condition for belonging of a function to the periodic generalized Nikol’skij-Besov-Morrey spaces.

Keywords

• Morrey space
• maximal function
• Fourier transform
• Nikol’skij-Besov-Morrey space