CHARACTERIZATION OF GENERALIZED HAUSDORFF OPERATOR ON VARIOUS INTEGRABLE SPACES

We characterize those R and positive Borel measure on (0, 1] for which generalized Hausdorff operator acts on Hardy spaces of the unit disk.Further, certain conditions on , we prove the operator is bounded linear on H p (D), for different cases of p.For = 0, we determine the characterization of the operator on weighted spaces of integrable functions.