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GENERALISED WEIGHTED COMPOSITION OPERATORS ON BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

Part of: Special classes of linear operators Spaces and algebras of analytic functions

Published online by Cambridge University Press:  08 January 2021

BIN LIU Open the ORCID record for BIN LIU [Opens in a new window]
BIN LIU*
Affiliation:
University of Eastern Finland, Joensuu P.O. Box 111, 80101, Finland
*
e-mail: binl@uef.fi
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Abstract

We characterise bounded and compact generalised weighted composition operators acting from the weighted Bergman space $A^p_\omega $ , where $0<p<\infty $ and $\omega $ belongs to the class $\mathcal {D}$ of radial weights satisfying a two-sided doubling condition, to a Lebesgue space $L^q_\nu $ . On the way, we establish a new embedding theorem on weighted Bergman spaces $A^p_\omega $ which generalises the well-known characterisation of the boundedness of the differentiation operator $D^n(f)=f^{(n)}$ from the classical weighted Bergman space $A^p_\alpha $ to the Lebesgue space $L^q_\mu $ , induced by a positive Borel measure $\mu $ , to the setting of doubling weights.

Keywords

Carleson measuredoubling weightsweighted Bergman spaceweighted composition operators

MSC classification

Primary: 47B33: Composition operators
Secondary: 30H20: Bergman spaces, Fock spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 1 , August 2021 , pp. 141 - 153
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This research was supported in part by the China Scholarship Council, No. 201706330108.

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