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arXiv · 2011.04699

Toeplitz operators on the unit ball with locally integrable symbols

Raffael Hagger·Congwen Liu·Jari Taskinen·Jani A. Virtanen
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Abstract

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.

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Raffael Hagger, Congwen Liu, Jari Taskinen, Jani A. Virtanen. 2020-11-09. Toeplitz operators on the unit ball with locally integrable symbols. https://arxiv.org/abs/2011.04699

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