Bounded, compact and Schatten class weighted composition operators between weighted Bergman spaces
Commun. Korean Math. Soc. 2011 Vol. 26, No. 3, 455-462
Printed September 1, 2011
Elke Wolf
University of Paderborn
Abstract : 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
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