  The aim of this paper is to study the sharp bounds of rough Hausdorff
operators on the product of Herz, central Morrey and Morrey-Herz spaces with
both power weights and Muckenhoupt weights on the Heisenberg group. Especially,
by applying the block decomposition of the Herz space, we obtain the
boundedness of rough Hausdorff operator in the case 0 < p < 1. In addition, the
boundedness for the commutators of rough Hausdorff operators on such spaces
with symbols in weighted central BMO space is also established.
