Copyright © 2009 Zhijie Jiang and Guangfu Cao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let denote the open unit disk in the complex plane and let denote the normalized area measure on . For and a twice differentiable, nonconstant, nondecreasing, nonnegative, and convex function on , the Bergman-Orlicz space is defined as follows Let be an analytic self-map of . The composition operator induced by is defined by for analytic in . We prove that the composition operator is compact on if and only if is compact on , and has closed range on if and only if has closed range on .