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Estimates on Bloch constants for certain log-p-harmonic mappings

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Abstract

In this paper, we first provide a brief overview of Landau-type theorems for log-p-harmonic mappings. Next, we establish four new versions of Landau-type theorems for certain bounded p-harmonic mappings F with \(J_F(0)=1\). Then, as applications of these results, the corresponding Landau-type theorems for certain log-p-harmonic mappings f with \(J_f(0)=1\) are provided. In particular, several sharp results of Landau-type theorems for certain bounded p-harmonic mappings or log-p-harmonic mappings with \(J_f(0)=1\) are obtained. Finally, we also establish a Landau-type theorem for a certain bounded log-p-harmonic mappings with \(J_f(0)=1\), which improves the corresponding results of different authors.

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Acknowledgements

The work of the first two authors are supported by Natural Science Foundation of Guangdong Province (Grant No. 2021A1515010058). The third author was supported by University of Macau (MYRG2022-00108-FST, MYRG-CRG2022–00010-ICMS), The Science and Technology Development Fund, Macau S.A.R (0036/2021/AGJ). The authors are grateful to the anonymous referee for making many suggestions that improved the readability of this paper.

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Authors and Affiliations

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

    Ming-Sheng Liu & Xin Wang

  2. Department of Mathematics, Shenzhen Polytechnic University, Shenzhen, 518055, Guangdong, China

    Xin Wang

  3. Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macao, China

    Kit Ian Kou

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  1. Ming-Sheng Liu
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  2. Xin Wang
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Correspondence to Ming-Sheng Liu.

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Liu, MS., Wang, X. & Kou, K.I. Estimates on Bloch constants for certain log-p-harmonic mappings. Monatsh Math 203, 175–198 (2024). https://doi.org/10.1007/s00605-023-01905-3

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