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Some inequalities for self-map**s of unit ball satisfying the invariant Laplacians

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Abstract

In this paper, we study those map**s in unit ball satisfying the Dirichlet problem of the following differential operators

$$\begin{aligned} \Delta _{\gamma }=\big (1-|x|^{2}\big )\cdot \left[ \frac{1-|x|^{2}}{4}\cdot \sum _{i}\frac{\partial ^{2}}{\partial x_{i}^{2}}+\gamma \sum _{i}x_{i}\cdot \frac{\partial }{\partial x_{i}}+\gamma \left( \frac{n}{2}-1-\gamma \right) \right] . \end{aligned}$$

Our aim is to establish the Schwarz type inequality, Heinz-Schwarz type inequality and boundary Schwarz inequality for those map**s.

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Acknowledgements

The authors would like to express their sincere thanks to the referees for their great efforts to improve this paper.

Funding

The first author was supported by Guangdong Basic and Applied Basic Research Foundation (No. 2022A1515110967; No. 2023A1515011809) and Research Foundation of Shenzhen Polytechnic University (No. 6023312032K). The third author was supported by Guangdong Province Higher Vocational Education Teaching Reform Research and Practice Project of in 2020 (No. JGGZKZ2020167).

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Authors and Affiliations

  1. Institute of Applied Mathematics, Shenzhen Polytechnic University, Shenzhen, 518055, Guangdong, People’s Republic of China

    Deguang Zhong, Meilan Huang & Dong** Wei

  2. Department of Applied Statistics, Guangdong University of Finance, Guangzhou, 510521, Guangdong, People’s Republic of China

    Deguang Zhong

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  1. Deguang Zhong
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  2. Meilan Huang
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Correspondence to Dong** Wei.

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Zhong, D., Huang, M. & Wei, D. Some inequalities for self-map**s of unit ball satisfying the invariant Laplacians. Monatsh Math 203, 911–925 (2024). https://doi.org/10.1007/s00605-023-01925-z

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  • DOI: https://doi.org/10.1007/s00605-023-01925-z

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