The Analytical Properties Of Some Function Spaces On The Unit Ball Of C～n

In this paper, the analytical properties of some function spaces on the unit ball of C~n(n＞1) are studied. We characterize Bloch type functions by higher radial derivative and obtain their characteristic of Carleson type measure. We study the inclusion relations betweenα-Bloch spaces and Dirichlet type spaces and show the strictness and the best possibility of these inclusions. Furthermore, we establish the characterization of Q_p functions by radial derivative and Carleson type measure, and give the sufficient condition of random power series in several complex variables which belong to Q_p spaces.