Some weighted inequalities for Hausdorff operators and commutators.

In this paper, we consider the problem of boundedness of Hausdorff operator on weighted central Morrey spaces. In particular, we obtain sharp bounds for Hausdorff operators on power weighted central Morrey spaces. Analogous results for the commutators of Hausdorff operators when the symbol functions belong to weighted central-BMO spaces are obtained as well.