数学物理学报 ›› 2017, Vol. 37 ›› Issue (1): 18-25.

• 论文 • 上一篇    下一篇

单位圆盘上全纯映照模的精细Schwarz引理

张宇芳, 徐庆华   

  1. 浙江科技学院理学院 杭州 310023
  • 收稿日期:2016-03-12 修回日期:2016-10-22 出版日期:2017-02-26 发布日期:2017-02-26
  • 通讯作者: 徐庆华 E-mail:xuqh@mail.ustc.edu.cn
  • 作者简介:张宇芳,E-mail:yfzhang@163.com
  • 基金资助:

    国家自然科学基金(11261022,11561030)、江西省自然科学基金(20152ACB20002,20161BAB201019)和江西省教育厅基金(GJJ150301)

Refinement of Schwarz Lemma for the Modulus of Holomorphic Mappings on the Unit Disk

Zhang Yufang, Xu Qinghua   

  1. School of Science, Zhejiang University of Science and Technology, Hangzhou 310023
  • Received:2016-03-12 Revised:2016-10-22 Online:2017-02-26 Published:2017-02-26
  • Supported by:

    Supported by NSFC (11261022, 11561030), the Jiangxi Provincial Natural Science Foundation (20152ACB20002, 20161BAB201019) and the Natural Science Foundation of Department of Education of Jiangxi Province (GJJ150301)

摘要:

记D∩C为单位圆盘,Bp={z∈Cn|zi|p<1},1 < p < +∞.该文证明了若fHm(D,Bp),则|▽||f||(z)|≤(m|z|m-1)/(1-|z|2m)(1-||fz)||2),z∈D.同时,当p为偶数时,该文也讨论了相应的极值问题,所得结论推广了一些相关结果.

关键词: 全纯映照, m阶零点, Schwarz引理

Abstract:

Let D be the unit disk in C, Bp={z∈Cn:|zi|p<1}, 1 < < +∞. In this note, it is proved that if fHm(D, Bp), then |▽||f||(z)|≤(m|z|m-1)/(1-|z|2m)(1-||f(z)||2),z∈D. The extremal problem is also discussed when p is an even number. This result extends some related results on schwarz lemma.

Key words: Holomorphic mappings, Zero of order m, Schwarz lemma

中图分类号: 

  • O174.56