Abstract
In this paper we consider Toepliz operators with (locally) integrable symbols acting on Bergman spaces $A^p$ ($1<p<\infty$) of the open unit disc of the complex plane. We give a characterization of compact Toeplitz operators with symbols in $L^1$ under a mild additional condition. Our result is new even in the Hilbert space setting of $A^2$, where it extends the well-known characterization of compact Toeplitz operators with bounded symbols by Stroethoff and Zheng.
Citation
Jari Taskinen. Jani Virtanen. "On compactness of Toeplitz operators in Bergman spaces." Funct. Approx. Comment. Math. 59 (2) 305 - 318, December 2018. https://doi.org/10.7169/facm/1727
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