Compact composition operators acting between weighted Bergman spaces of the unit ball

In this paper, we study a composition operator ${C_{\varphi}}$ on the weighted Bergman space ${A_{\alpha}^p(B)}$ of the unit ball B in ${{\mathbb{C}}^N}$ . Under a natural condition we estimate the essential norm of ${C_{\varphi}}$ . As a consequence of this estimate, we also give a function-theoretic characterization of ${\varphi}$ that induces a compact composition operator on ${A_{\alpha}^p(B)}$ .