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Weighted Space and Bloch-Type Space on the Unit Ball of an Infinite Dimensional Complex Banach Space

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Abstract

Let \({\mathbf {B}}_{{\mathbb {X}}}\) be the open unit ball of a complex Banach space \({\mathbb {X}}\), which may beinfinite dimensional. The weighted composition operator and weighted space defined on \({\mathbf {B}}_{{\mathbb {X}}}\) are introduced. We obtain the boundedness and compactness of the weightedcomposition operator from the Bloch-type spaces to the weighted spaces, and some properties with the Bloch-type spaces are given. Our main results generalize theprevious works on the Euclidean unit ball \({\mathbb {B}}^n\) to the case of \({\mathbf {B}}_{{\mathbb {X}}}\).

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Acknowledgements

The project is supported by the National Natural Science Foundation of China (no. 11671306).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, People’s Republic of China

    Zhenhan Tu & Liangpeng Xiong

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  1. Zhenhan Tu
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  2. Liangpeng Xiong
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Correspondence to Liangpeng Xiong.

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Communicated by Ali Abkar.

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Tu, Z., Xiong, L. Weighted Space and Bloch-Type Space on the Unit Ball of an Infinite Dimensional Complex Banach Space. Bull. Iran. Math. Soc. 45, 1389–1406 (2019). https://doi.org/10.1007/s41980-019-00204-8

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  • DOI: https://doi.org/10.1007/s41980-019-00204-8

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