Schatten classes of Toeplitz operators on Bergman-Besov Hilbert spaces in the unit ball

Yang, Wenwan; Liu, Junming

doi:10.1016/j.jmaa.2023.127257

Journal of Mathematical Analysis and Applications

2023

DOI: 10.1016/j.jmaa.2023.127257

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Schatten classes of Toeplitz operators on Bergman-Besov Hilbert spaces in the unit ball

Wenwan Yang

Junming Liu

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2023

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Schatten class composition operators on the Hardy space

Yang¹,

Yuan²

2023

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Suppose $2< p<\infty$ and $\varphi$ is a holomorphic self-map of the open unit disk $\mathbb {D}$ . We show the following assertions: (1) If $\varphi$ has bounded valence and 0.1 \begin{equation} \int_{\mathbb{D}} \left(\frac{1-|z|^2}{1-|\varphi(z)|^2}\right)^{p/2}\frac{\mathrm{d} A(z)}{(1-|z|^2)^2}<\infty, \end{equation} then $C_{\varphi }$ is in the Schatten $p$ -class of the Hardy space $H^2$ . (2) There exists a holomorphic self-map $\varphi$ (which is, of course, not of bounded valence) such that the inequality (0.1) holds and $C_{\varphi }: H^2\to H^2$ does not belong to the Schatten $p$ -class.

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Schatten class composition operators on the Hardy space

Yang¹,

Yuan²

2023

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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show abstract

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Schatten classes of Toeplitz operators on Bergman-Besov Hilbert spaces in the unit ball

Cited by 1 publication

References 8 publications

Schatten class composition operators on the Hardy space

Schatten class composition operators on the Hardy space

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