Boundedness of Marcinkiewicz Integrals in Weighted Variable Exponent Herz-Morrey Spaces (Communications in Mathematical Research, 2019)
In this paper, under natural regularity assumptions on the exponentfunction, we prove some boundedness results for the functions of Littlewood-Paley,Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weightand variable exponent, which essentially extends some known results.
Keywords: Marcinkiewicz integral; variable exponent; Muckenhoupt weight; Herz-Morrey space