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http://dx.doi.org/10.4134/CKMS.2011.26.3.455

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

Wolf, Elke (Mathematical Institute University of Paderborn)
Publication Information
Communications of the Korean Mathematical Society / v.26, no.3, 2011 , pp. 455-462 More about this Journal
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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