| 一类单叶调和函数的拟共形性质 |
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| 引用本文： | 傅冬绵1,黄心中2. 一类单叶调和函数的拟共形性质[J]. 华侨大学学报(自然科学版), 2019, 0(6): 812-816. DOI: 10.11830/ISSN.1000-5013.201903003 |
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| 作者姓名： | 傅冬绵1 黄心中2 |
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| 作者单位： | 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 |
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| 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f(z)=h(z)+g(z)^-的拟共形性质,对复伸张w(z)=(g’(z))/(h’(z))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Dc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.
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| 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 |
On Quasiconformal Properties for One Set of Univalent Harmonic Mappings |
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| FU Dongmian1,HUANG Xinzhong2. On Quasiconformal Properties for One Set of Univalent Harmonic Mappings[J]. Journal of Huaqiao University(Natural Science), 2019, 0(6): 812-816. DOI: 10.11830/ISSN.1000-5013.201903003 |
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| Authors: | FU Dongmian1 HUANG Xinzhong2 |
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| Affiliation: | 1. College of Business Administration, Huaqiao University, Quanzhou 362021, China; 2. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China |
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| Abstract: | We study the quasiconformal properties of the univalent harmonic functions f(z)=h(z)+g(z)^- 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 w(z)=(g’(z))/(h’(z)). Moreover, we construct their harmonic quasiconformal extension functions to the domain Dc 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. |
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| Keywords: | univalent harmonic function quasiconformal mapping module estimate of complex dilatation harmonic quasiconformal extension |
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