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BOUNDED, COMPACT AND SCHATTEN CLASS WEIGHTED COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

Wolf, Elke

  • Received : 2007.10.25
  • Published : 2011.07.31

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 $C_{{\phi},{\psi}}$: $H(\mathbb{D})\;{\rightarrow}\;H(\mathbb{D})$, $f{\mapsto} \;{\psi}\;(f\;o\;{\phi})$, 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

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  1. ORDER BOUNDED WEIGHTED COMPOSITION OPERATORS vol.93, pp.03, 2012, https://doi.org/10.1017/S1446788712000316