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Fekete and Szegö problem in one and higher dimensions

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Abstract

In this paper, we establish the Fekete and Szegö inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in \(\mathbb{C}^n\).

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11561030, 11261022 and 11471111), the Jiangxi Provincial Natural Science Foundation of China (Grant Nos. 20152ACB20002 and 20161BAB201019) and Natural Science Foundation of Department of Education of Jiangxi Province of China (Grant No. GJJ150301).

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Authors and Affiliations

  1. School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023, China

    Qinghua Xu

  2. Department of Mathematics, Huzhou University, Huzhou, 313000, China

    Taishun Liu

  3. School of Mathematics and Computation Science, Lingnan Normal University, Zhanjiang, 524048, China

    Xiaosong Liu

Authors
  1. Qinghua Xu
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  2. Taishun Liu
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  3. Xiaosong Liu
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Correspondence to Qinghua Xu.

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Xu, Q., Liu, T. & Liu, X. Fekete and Szegö problem in one and higher dimensions. Sci. China Math. 61, 1775–1788 (2018). https://doi.org/10.1007/s11425-017-9221-8

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  • DOI: https://doi.org/10.1007/s11425-017-9221-8

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