Weighted Morrey estimates for Hausdorff operator and its commutator on the Heisenberg group

In this paper, we study the high-dimensional Hausdorff operators, defined via a general linear mapping $A$, and their commutators on the weighted Morrey spaces in the setting of the Heisenberg group. Particularly, under some assumption on the mapping $A$, we establish their sharp boundedness on the power weighted Morrey spaces.