Boundedness of Marcinkiewicz Integrals in Weighted Variable Exponent Herz-Morrey Spaces

Abstract

In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extends some known results.