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 NameAffiliation
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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