一类单叶调和函数的拟共形性质  

On Quasiconformal Properties for One Set of Univalent Harmonic Mappings

作　　者：傅冬绵[1] 黄心中[2] FU Dongmian;HUANG Xinzhong(College of Business Administration,Huaqiao University,Quanzhou 362021,China;School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学工商管理学院,福建泉州362021 [2]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2019年第6期812-816,共5页Journal of Huaqiao University(Natural Science)

基　　金：华侨大学中青年教师科技创新资助项目(600005-Z16J063)

摘　　要：研究单位圆盘D={z‖z|<1}上满足Re{αz[h″(z)+g″(z)]+h′(z)+g′(z)}>0,z∈D,α>0的单叶调和函数■的拟共形性质,对复伸张■的模给出最好的最小上界估计,进而给出该类函数到D的余集D^c上的拟共形延拓,并对其复伸张的模给出最好的最小上界估计,改进和推广了2004年Yalcin S等的研究成果.We study the quasiconformal properties of the univalent harmonic functions ■ on the unit disk D={z‖z|<1} with Re{αz[h″(z)+g″(z)]+h′(z)+g′(z)}>0, z∈D, α>0, and obtain the best upper bound estimation for the module of the dilatation function ■. Moreover, we construct their harmonic quasiconformal extension functions to the domain D^c of D, and give the best upper bound estimation for the module of their dilatation functions. The results improve and generalize the ones made by Yalcin S, et al in 2004.

关 键 词：单叶调和函数 拟共形映照 复特征模估计 调和拟共形延拓 

分 类 号：O174.51[理学—数学] O174.55[理学—基础数学]