Abstract

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

Keywords: Hausdorff matrix; Cesàro operator; Hardy spaces; weighted spaces.

MSC: 47B38, 46E15

DOI: 10.57016/MV-2KMB8y81

Pages:  29--37     

Volume  77 ,  Issue  1 ,  2025