Hausdorff Operators In Hardy Spaces On Cartan Type Domains In C-N

The main results of the present paper are two-fold. Firstly, they describe a broad class of bounded domains D subset of C-n allowing to decide, by elementary inductive means, whether a holomorphic function f in D belongs to the corresponding Hardy space H-P(D), p > 0. Secondly, based on previous results, we define for such domains the corresponding Hausdorff operators and formulate sufficient conditions for such operators to be bounded. Similar results are also given for Bergman spaces.