Weighted composition operators on weighted Bergman spaces of the unit ball (Q2914809)

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scientific article; zbMATH DE number 6084639
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Weighted composition operators on weighted Bergman spaces of the unit ball
scientific article; zbMATH DE number 6084639

    Statements

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    21 September 2012
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    composition operator
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    weighted composition operator
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    weighted Bergman space
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    Schatten class operators
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    Carleson measures
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    Weighted composition operators on weighted Bergman spaces of the unit ball (English)
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    Let \(B_n\) denote the unit ball in \(\mathbb{C}^n\). The paper considers weighted composition operators \(W_{\psi,\phi}f(z)=\psi(z)f(\phi(z))\) from a weighted Bergman space \(A^p_\alpha\) to another weighted Bergman space \(A^q_\beta\). Characterizations of boundedness, compactness, and membership in Schatten classes are obtained in terms Carleson-type measures and Berezin-type transforms.
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