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

Title & Authors
BOUNDED, COMPACT AND SCHATTEN CLASS WEIGHTED COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES
Wolf, Elke;

Abstract
An analytic self-map $\small{{\phi}}$ of the open unit disk $\small{\mathbb{D}}$ in the complex plane and an analytic map $\small{{\psi}}$ on $\small{\mathbb{D}}$ induce the so-called weighted composition operator $\small{C_{{\phi},{\psi}}}$: $\small{H(\mathbb{D})\;{\rightarrow}\;H(\mathbb{D})}$, $\small{f{\mapsto} \;{\psi}\;(f\;o\;{\phi})}$, where H($\small{\mathbb{D}}$) denotes the set of all analytic functions on $\small{\mathbb{D}}$. We study when such an operator acting between different weighted Bergman spaces is bounded, compact and Schatten class.
Keywords
weighted Bergman space;composition operator;
Language
English
Cited by
1.
ORDER BOUNDED WEIGHTED COMPOSITION OPERATORS, Journal of the Australian Mathematical Society, 2012, 93, 03, 333
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