| 单位球上全纯函数的高阶Schwarz-Pick估计* |
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| 引用本文： | 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(中文版),2021,42(3):269-278. |
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| 作者姓名： | 李锦成 石擎天 王建飞 |
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| 作者单位： | 华侨大学数学科学学院, 福建 泉州 362021; 华侨大学计算科学福建省高校重点实验室,福建 泉州 362021.;泉州师范学院数学与计算机科学学院, 福建 泉州 362000;泉州师范学院 福建省大数据管理新技术与知识工程重点实验室,福建 泉州 362000. |
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| 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) |
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| 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.
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| 关 键 词： | Schwarz-Pick 估计 系数估计 双曲度量 凸区域 |
| 收稿时间： | 2019/12/4 0:00:00 |
| 修稿时间： | 2020/11/22 0:00:00 |
Schwarz-Pick Estimates for Holomorphic Functions on the Unit Ball |
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| LI Jincheng,SHI Qingtian,WANG Jianfei.Schwarz-Pick Estimates for Holomorphic Functions on the Unit Ball[J].Chinese Annals of Mathematics,2021,42(3):269-278. |
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| Authors: | LI Jincheng SHI Qingtian WANG Jianfei |
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| Institution: | School of Mathematics Sciences, Huaqiao University, Quanzhou 362021, Fujian,China; Fujian Province University Key Laboratory of Computational Science,Huaqiao University, Quanzhou 362021, Fujian, China.;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. |
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| Abstract: | 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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| Keywords: | Schwarz-Pick estimates Coefficient estimates Hyperbolic metric Convex domain |
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