Boundedness of some sublinear operators on Herz–Morrey spaces with variable exponent

Abstract

In this paper, the boundedness of some sublinear operators is proved on homogeneous Herz-Morrey spaces with variable exponent.

Hardy’s inequalities and integral operators on Herz-Morrey spaces

“…One of the pioneer studies on the Herz-Morrey spaces is from Lu and Xu [7] on the mapping properties of the singular integral operators on the Herz-Morrey spaces. Since then, the study of Herz-Morrey spaces inspires the introduction of a number of new function spaces including Herz-Morrey-Hardy spaces [8,9], Herz-Morrey spaces with variable exponents [10][11][12][13][14][15] and the Herz-Morrey-Besov spaces [16].…”