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Bloch Type Spaces on the Unit Ball of a Hilbert Space

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Abstract

We initiate the study of Bloch type spaces on the unit ball of a Hilbert space. As applications, the Hardy-Littlewood theorem in infinite-dimensional Hilbert spaces and characterizations of some holomorphic function spaces related to the Bloch type space are presented.

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Acknowledgment

The main result of this work is part of the author’s Ph.D. thesis completed in November 2016. The author is very grateful to his advisor for helpful discussions and to the anonymous referees for valuable suggestions for the improvement of the manuscript.

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, No. 420 Feicui Road, Hefei, Anhui, 230601, P.R. China

    Zhenghua Xu

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  1. Zhenghua Xu
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Correspondence to Zhenghua Xu.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11801125) and the Fundamental Research Funds for the Central Universities (Nos. JZ2018HGBZ0118 and JZ2018HGTA0199).

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Xu, Z. Bloch Type Spaces on the Unit Ball of a Hilbert Space. Czech Math J 69, 695–711 (2019). https://doi.org/10.21136/CMJ.2018.0495-17

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  • DOI: https://doi.org/10.21136/CMJ.2018.0495-17

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