Toeplitz operators on the unit ball with locally integrable symbols

2020/11/09 by Raffael Hagger, Hagger, Raffael, Congwen Liu +5
Mathematics · #47B35 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2011.04699

openalex publication_date 2020/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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