Hausdorff–Berezin and Hausdorff–Zhu Operators on Bidisc

The article introduces and studies Hausdorff–Berezin andHausdorff–Zhu type operators on bidisc. These operators arenatural generalization of the Berezin transform and some otherclassical operators of mathematical physics. Sufficient andnecessary conditions for boundedness of such operators in themixed norm weighted Lebesgue type spaces are given. We also studythe question of identity approximations by such operators in themixed norm weighted Lebesgue type spaces on bidisc.