Toeplitz operators on the unit ball with locally integrable symbols

Hagger, R., Liu, C., Taskinen, J. and Virtanen, J. A. (2022) Toeplitz operators on the unit ball with locally integrable symbols. Integral Equations and Operator Theory, 94 (2). 17. ISSN 0378-620X doi: 10.1007/s00020-022-02695-3

Abstract/Summary

We study the boundedness of Toeplitz operators Tψ with locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of R n. Generalizing earlier results for analytic function spaces, we derive a general sufficient condition for the boundedness of Tψ 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.