Composition operators on weighted Bergman-Orlicz spaces

In this paper, composition operators acting on Bergman-Orlicz spaces A(alpha)(Psi) = {f epsilon H(D) : parallel to f parallel to(Psi)(A alpha) = integral(D) Psi(log vertical bar f(z)vertical bar)dv alpha(z) < infinity} are studied, where Psi is a non-constant, non-decreasing convex function defined on (-infinity, infinity) which satisfies the growth condition lim/(t ->infinity) Psi (t)/t = infinity. In fact, under a mild condition on Psi, we show that every holomorphic-self map theta of D induces a bounded composition operator on A(alpha)(Psi) and C-phi is compact on A(alpha)(Psi) if and only if it is compact on a A(alpha)(2).