ANALYSIS OF SOME FUNCTION SPACES ASSOCIATED TO HANKEL OPERATORS

摘要

Generally speaking, it may be said that a significant part of the analysis of (holo-morphic) Bergman spaces on a bounded domain D is contained in C~n can be understood by the device of restricting to D the corresponding holomorphic Hardy spaces on a suitable domain in C~(n+1). These ideas have been used in several papers, including Forelli [FOR], Rudin [RUD], Coifman, Rochberg and Weiss [CRW], Beatrous and Burbea [BEB], Ligocka [LIG], and references therein. The main point of the present paper is to give several examples which develop this point of view. Our aim will be to extend these ideas to the real Hardy spaces so that we may obtain related results on the "real Bergman spaces" L_b~p(D) by using known results on real Hardy spaces.