COMPACT COMPOSITION OPERATORS ON THE WEIGHTED BERGMAN SPACES OF THE UNIT BALL
单位球上的加权Bergman空间上的紧复合算子

Under a mild condition it is shown that a composition operator $C_{\varphi}$ is compact on the weighted Bergman space $A^{p}(\phi)$ of the open unit ball in $\mathbb{C}^{n}$ if and only if $ {{1-|z|^{2}} \over {1-|\varphi(z)|^{2}}}\rightarrow 0$ as $|z|\rightarrow 1^{-}$.