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Weighted Composition Operators from the Bloch Spaces to Weighted Hardy Spaces on Bounded Symmetric Domains

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Abstract

Let \(\mathbb{B}_{E}\) be a bounded symmetric domain realized as the unit open ball of JB*-triples. The authors will characterize the bounded weighted composition operator from the Bloch space \(\cal{B}(\mathbb{B}_{E})\) to weighted Hardy space \(H_{v}^{\infty}(\mathbb{B}_{E})\) in terms of Kobayashi distance. The authors also give a sufficient condition for the compactness, and also give the upper bound of its essential norm. As a corollary, they show that the boundedness and compactness are equivalent for composition operator from \(\cal{B}(\mathbb{B}_{E})\) to \(H^{\infty}(\mathbb{B}_{E})\), when E is a finite dimension JB*-triple. Finally, they show the boundedness and compactness of weighted composition operators from \(H_{v}^{\infty}(\mathbb{B}_{E})\) to \(H_{v,0}^{\infty}(\mathbb{B}_{E})\) are equivalent when E is a finite dimension JB*-triple.

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Acknowledgement

The authors would like to thank the referee for useful suggestions which improved the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Lei Li & Xiao Wang

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  1. Lei Li
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  2. Xiao Wang
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Correspondence to Lei Li or Xiao Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 12171251).

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Li, L., Wang, X. Weighted Composition Operators from the Bloch Spaces to Weighted Hardy Spaces on Bounded Symmetric Domains. Chin. Ann. Math. Ser. B 44, 289–298 (2023). https://doi.org/10.1007/s11401-023-0015-z

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  • DOI: https://doi.org/10.1007/s11401-023-0015-z

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