Communications of the
Korean Mathematical Society CKMS

An analytic self-map $\phi$ of the open unit disk $\mathbb D$ in the complex plane and an analytic map $\psi$ on $\mathbb D$ induce the so-called weighted composition operator $C_{\phi,\psi}: H(\mathbb D) \to H(\mathbb D), \; f \mapsto \psi (f \circ \phi)$, where $H(\mathbb D)$ denotes the set of all analytic functions on $\mathbb D$. We study when such an operator acting between different weighted Bergman spaces is bounded, compact and Schatten class.

Keywords: weighted Bergman space, composition operator

MSC numbers: 47B33, 47B38