On a class of Hausdorff–Berezin operators on the unit disc

We introduce and study the class of Hausdorff-Berezin operators on the unit disc in the Lebesgue $p$-spaces with Haar measure. We discuss certain algebraic properties of such operators, and also give sufficient, and, in some cases necessary boundedness conditions for such operators. Joint work with Profs. K. Zhu and S. Samko.