Abstract. In this paper, we study a weighted composition operator $uC_{\varphi }$ on the weighted Bergman space $L_{a}^2(dA_{\alpha })$ of the unit disc ${\msbm D}$. We estimate the essential norm of this type of operator. As a consequence of this estimate, we give a function-theoretic characterization of $u$ and $\varphi $ that induce a compact weighted composition operator on $L_{a}^2(dA_{\alpha })$.

AMS Subject Classification (1991): 47B38, 47B33

Keyword(s): weighted composition operator, Bergman space

Received July 23, 2008, and in revised form February 23, 2009. (Registered under 6436/2009.)