Hardy operators on weighted Herz–Morrey spaces

Abstract

This paper extends the boundedness of the higher-dimensional Hardy operator and the higher-dimensional adjoint Hardy operator to the weighted Herz–Morrey spaces. As special cases of our main results, we also have the boundedness of the higher-dimensional Hardy operator and the higher-dimensional adjoint Hardy operator to the weighted Herz spaces. We obtain these results by extending the boundedness of the higher-dimensional Hardy operator and the higher-dimensional adjoint Hardy operator on the weighted Lebesgue spaces.