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On pluriharmonic \(\nu \)-Bloch-type mappings and hyperbolic-harmonic mappings

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Abstract

In this paper, we first establish a new version of Landau-type theorem of pluriharmonic mappings in the unit ball of \({\mathbb {R}}^{2n}\). Next we obtain a Bloch theorem of pluriharmonic \(\nu \)-Bloch-type mappings. Then, we provide a necessary condition for the hyperbolic-harmonic \(\nu \)-Bloch mappings in the unit ball of \({\mathbb {C}}^n\). Finally, we obtain a sufficient and necessary condition for the hyperbolic-harmonic \(\nu \)-Bloch mappings for the case of \(0<\nu \le 1\), which generalizes a result of Chen et al. (Math Model Anal 18:66–79, 2012).

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, Guangdong, China

    Zhi-Fei Xu & Ming-Sheng Liu

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  1. Zhi-Fei Xu
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  2. Ming-Sheng Liu
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Correspondence to Ming-Sheng Liu.

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Communicated by Adrian Constantin.

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This research is supported by Guangdong Natural Science Foundation (Grant No. 2018A030313508).

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Xu, ZF., Liu, MS. On pluriharmonic \(\nu \)-Bloch-type mappings and hyperbolic-harmonic mappings. Monatsh Math 192, 965–978 (2020). https://doi.org/10.1007/s00605-019-01351-0

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