Hausdorff–Berezin and Hausdorff–Zhu Operators onBidisc

The article introduces and studies Hausdorff–Berezin and Hausdorff–Zhu type operators on bidisc. These operators are natural generalization of the Berezin transform and some other classical operators of mathematical physics. Sufficient and necessary conditions for boundedness of such operators in the mixed norm weighted Lebesgue type spaces are given. We also study the question of identity approximations by such operators in the mixed norm weighted Lebesgue type spaces on bidisc.