Toeplitz operators on the unit ball with locally integrable symbols

We study the boundedness of Toeplitz operators \(T_\psi\) with locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of \(\mathbb{R}^n\). Generalizing earlier results for analytic function spaces, we derive a general sufficient condition for the boundedness of \(T_\psi\)...

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Bibliographic Details
Published in:arXiv.org 2022-03
Main Authors: Hagger, Raffael, Liu, Congwen, Taskinen, Jari, Virtanen, Jani A
Format: Article
Language:English
Subjects:
Analytic functions
Function space
Operators (mathematics)
Symbols
Online Access:Get full text
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Summary:We study the boundedness of Toeplitz operators \(T_\psi\) with locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of \(\mathbb{R}^n\). Generalizing earlier results for analytic function spaces, we derive a general sufficient condition for the boundedness of \(T_\psi\) in terms of suitable averages of its symbol. We also obtain a similar "vanishing" condition for compactness. Finally, we show how these results can be transferred to the setting of the standard weighted Bergman spaces of analytic functions.
ISSN:2331-8422