Karapetyants, AlexeySamko, StefanZhu, Kehe2020-07-242020-07-242019-111661-8254http://hdl.handle.net/10400.1/14184We introduce and study a class of Hausdorff-Berezin operators on the unit disc based on Haar measure (that is, the Mobius invariant area measure). We discuss certain algebraic properties of these operators and obtain boundedness conditions for them. We also reformulate the obtained results in terms of ordinary area measure.engHardy-spacesBoundednessDomainsHausdorff operatorsBerezin transformBergman kernelInvariant kernelHaar measureMobius groupjournal article10.1007/s11785-019-00934-x