Boundedness of Singular Integral Operators on Herz-Morrey Spaces with Variable Exponent

Abstract

In this paper, the authors define the weak Herz spaces and the weak Herz-type Hardy spaces with variable exponent. As applications, the authors establish the boundedness for a large class of singular integral operators including some critical cases.

A Characterization of Boundedness of Fractional Maximal Operator with Variable Kernel on Herz-Morrey Spaces

“…Boundedness of fractional Marcinkiewicz integral with variable kernel on variable exponent Morrey-Herz spaces was given by [3]. We also note that Herz-Morrey spaces with variable exponent are generalization of Morrey-Herz spaces [8] and Herz spaces with variable exponent [8,13]. Our main goal is to give a characterization on boundedness of the fractional maximal operator with variable kernel from MH β,α…”