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In this paper, we give necessary and sufficient conditions for theboundedness of rough Hausdorff operators on Herz, Morrey and Morrey-Herz spaceswith absolutely homogeneous weights. Especially, the estimates for operatornorms in each case are worked out. Moreover, we also establish the boundednessof the commutators of rough Hausdorff operators on the such spaces with theirsymbols belonging to Lipschitz space.

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