Weak Estimates for the Maximal and Riesz Potential Operators in Central Herz–Morrey Spaces on the Unit Ball

Abstract

Morrey spaces are the powerful tool for the study of partial differential equations. Recently, weak Morrey spaces and weak Herz spaces are known to be useful for the study of Navier–Stokes equations. In this paper we introduce weak central Herz–Morrey spaces $W{\mathcal{H}}^{p(\cdot ),q,\omega }(\mathbf{B})$ and establish the weak estimate for the maximal and Riesz potential operators in the central Herz–Morrey space ${\mathcal{H}}^{p(\cdot ),q,\omega }(\mathbf{B})$. We also treat generalized Riesz potential operators. Further we obtain the strong estimate for Sobolev functions.