Weighted norm inequalities for rough Hausdorff operator and its commutators on the Heisenberg group

Abstract: 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.