Weighted Morrey–Herz space estimates for rough Hausdorff operator and its commutators

Abstract

In this paper, we give necessary and sufficient conditions for the boundedness of rough Hausdorff operators on Herz, Morrey and Morrey–Herz spaces with absolutely homogeneous weights. Especially, the estimates for operator norms in each case are worked out. Moreover, we also establish the boundedness of the commutators of rough Hausdorff operators on the two weighted Morrey–Herz type spaces with their symbols belonging to Lipschitz space. By these, we obtain some new estimates for the high dimensional Hardy operator and adjoint Hardy operator.