数学物理学报(英文版) ›› 2026, Vol. 46 ›› Issue (1): 131-144.doi: 10.1007/s10473-026-0109-2

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SCHWARZ TYPE LEMMAS FOR QUATERNION $k$-REGULAR FUNCTIONS

Xiaotong LIANG, Xiaojing DU, Yonghong XIE*   

  1. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, China
  • 收稿日期:2024-06-15 修回日期:2024-11-06 出版日期:2026-01-25 发布日期:2026-05-22

SCHWARZ TYPE LEMMAS FOR QUATERNION $k$-REGULAR FUNCTIONS

Xiaotong LIANG, Xiaojing DU, Yonghong XIE*   

  1. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, China
  • Received:2024-06-15 Revised:2024-11-06 Online:2026-01-25 Published:2026-05-22
  • Contact: * Yonghong Xie, E-mail: xyh1973@126.com
  • About author:Xiaotong Liang, E-mail: lxt139@126.com; Xiaojing Du, E-mail: 15203219474@163.com
  • Supported by:
    Innovation Foundation of the School of Mathematical Sciences in Hebei Normal University in 2025 (ycxzzbs202503), the NSF of Hebei Province (A2023205006, A2022208007, A2023205045, A2024208005), the Hebei Research Center of the Basic Discipline Pure Mathematics, the Key Development Foundation of Hebei Normal University (L2024ZD08), the NSFC (12431005), and the Funding Project of Central Guidance for Local Scientific and Technological Development (246Z7608G).

摘要: In this paper, Schwarz-type lemmas for different classes of quaternion functions are obtained. Firstly, some properties of symmetric points are given. Secondly, the Schwarz-type lemma and the Schwarz-Pick-type theorem for quaternion regular functions are obtained. Finally, the Schwarz-type lemma for quaternion $k$-regular functions is derived.

关键词: quaternion, Schwarz-type lemma, Schwarz-Pick lemma, Poisson integral formula

Abstract: In this paper, Schwarz-type lemmas for different classes of quaternion functions are obtained. Firstly, some properties of symmetric points are given. Secondly, the Schwarz-type lemma and the Schwarz-Pick-type theorem for quaternion regular functions are obtained. Finally, the Schwarz-type lemma for quaternion $k$-regular functions is derived.

Key words: quaternion, Schwarz-type lemma, Schwarz-Pick lemma, Poisson integral formula

中图分类号: 

  • 30G35