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arXiv · 2002.06771

Toeplitz operators on weighted Bergman spaces induced by a class of radial weights

Yongjiang Duan·Kunyu Guo·Siyu Wang·Zipeng Wang
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Abstract

Suppose that $\omega$ is a radial weight on the unit disk that satisfies both forward and reverse doubling conditions. Using Carleson measures and $T1$-type conditions, we obtain necessary and sufficient conditions of the positive Borel measure $\mu$ such that the Toeplitz operator $T_{\mu,\omega}:L^p_a(\omega)\to L_a^1(\omega)$ is bounded and compact for $0<p\leq 1$. In addition, we obtain a bump condition for the bounded Toeplitz operators with $L^1(\omega)$ symbol on $L^1_a(\omega)$. This generalizes a result of Zhu in \cite{zhu1989}.

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Yongjiang Duan, Kunyu Guo, Siyu Wang, Zipeng Wang. 2020-02-17. Toeplitz operators on weighted Bergman spaces induced by a class of radial weights. https://arxiv.org/abs/2002.06771

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