Mapping properties for operators on Herz-Morrey and Herz-Morrey-Hardy spaces

In this paper, we bulid the extrapolation theory for Herz-Morrey spaces, from which the mapping properties of the parametric Marcinkiewicz integrals, the geometric maximal operator, the minimal operator and the Rubio de Francia inequalities on Herz-Morrey spaces are deduced. By extending the extrapolation theory to Herz-Morrey-Hardy spaces, we also obtain the boundedness of the singular integral operators and the maximal Bochner-Riesz means on Herz-Morrey-Hardy spaces.