  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 such spaces with their
symbols belonging to Lipschitz space.
