| 李锦成,石擎天,王建飞.单位球上全纯函数的高阶Schwarz-Pick估计*[J].数学年刊A辑,2021,42(3):269~278 |
| 单位球上全纯函数的高阶Schwarz-Pick估计* |
| Schwarz-Pick Estimates for Holomorphic Functions on the Unit Ball |
| Received:December 04, 2019 Revised:November 22, 2020 |
| DOI：10.16205/j.cnki.cama.2021.0021 |
| 中文关键词: Schwarz-Pick 估计, 系数估计, 双曲度量, 凸区域 |
| 英文关键词:Schwarz-Pick estimates, Coefficient estimates, Hyperbolic metric,Convex domain |
| 基金项目:国家自然科学基金(No.11671362, No.12071161, No.11971165),福建省自然科学基金(No.2020J010731, No.2020J05157, No.2019J01066),福建省教育厅中青年科研项目(No.JAT190508)和泉州市高层次人才团队项目(No.20172T012) |
| Author Name | Affiliation | | LI Jincheng | School of Mathematics Sciences, Huaqiao University, Quanzhou 362021, Fujian,China
Fujian Province University Key Laboratory of Computational Science,Huaqiao University, Quanzhou 362021, Fujian, China. | | SHI Qingtian | Corresponding author. School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, Fujian, China
Fujian Provincial Key Laboratory of Data Intensive Computing, Quanzhou Normal University, Quanzhou 362000, Fujian, China. | | WANG Jianfei | School of Mathematics Sciences, Huaqiao University, Quanzhou 362021, Fujian,China
Fujian Province University Key Laboratory of Computational Science,Huaqiao University, Quanzhou 362021, Fujian, China. |
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| 中文摘要: |
| 作者给出了单位球Bn ? Cn到凸区域?? C上全纯函数的高阶Schwarz-Pick估计. 通过引入双曲度量,得到了单位圆盘D到凸区域?上全纯函数的系数估计. 应用该系数估计结果,得到单位球Bn到?内的全纯函数的高阶Schwarz-Pick估计.特别地, 当?是单位圆盘或右半平面时, 得到的结果分别与熟知的结果是一致的. |
| 英文摘要: |
| In this paper, the authors establish higher order Schwarz-Pick estimates of holomorphic functions which map the unit ball Bn of Cn into a convex subdomain ? of C. By introducing the hyperbolic metric, they obtain the standard coefficient estimates for holomorphic functions from the unit disk D into the convex domain ? in C. As applications,they obtain the higher order Schwarz-Pick estimates for holomorphic functions from Bn into ?. When ? is the unit disk or the right half-plane, the results reduce to some known results,respectively |
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