| Hartogs域上延拓算子的性质 |
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| 引用本文： | 崔艳艳,刘浩. Hartogs域上延拓算子的性质[J]. 数学年刊A辑(中文版), 2019, 40(2): 139-156 |
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| 作者姓名： | 崔艳艳 刘浩 |
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| 作者单位： | 周口师范学院数学与统计学院, 河南 周口 466001.,通信作者. 河南大学数学系, 河南 开封 475001. |
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| 基金项目： | 本文受到国家自然科学基金(No.11271359,No.11471098),河南省教育厅科学技术研究重点项目(No.17A110041)和周口师范学院科研创新基金项目(No.ZKNUA201805)的资助. |
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| 摘 要： | 主要研究Roper-Suffridge延拓算子在推广的Hartogs域上的性质.借助双全纯映照的偏差定理,得到延拓算子在Ω_N上保持强α次殆β型螺形映照、α次殆β型螺形映照和α次β型螺形映照的性质,进而得到B~n上相应的结论.所得结论包含已有的结果并为研究C~n中的双全纯映照提供了新的途径.
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| 关 键 词： | Starlike mappings Spirallike mappings Extension operators |
| 收稿时间： | 2017-05-08 |
| 修稿时间： | 2018-08-19 |
Properties of the Perturbed Extension Operators on Hartogs Domains |
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| CUI Yanyan and LIU Hao. Properties of the Perturbed Extension Operators on Hartogs Domains[J]. Chinese Annals of Mathematics, 2019, 40(2): 139-156 |
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| Authors: | CUI Yanyan and LIU Hao |
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| Affiliation: | College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, Henan, China. and Corresponding author. Department of Mathematics, Henan University, Kaifeng 475001, Henan, China. |
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| Abstract: | This paper mainly discuss the properties of the generalized Roper-Suffridgeoperators on the extended Hartogs domains. By using the distortionresults of subclasses of biholomorphic mappings, the authors conclude thatthe generalized operators preserve the properties of strong andalmost spirallike mappings of type $beta$ and order $alpha$,almost spirallike mappings of type $beta$ and order $alpha$,spirallike mappings of type $beta$ and order $alpha$ on $Omega_N$under different conditions, respectively. Thus the authors get thecorresponding results on $B^n$. These conclusions involve some knownresults and provide new approaches to research the biholomorphicmappings in $mathbb{C}^n$. |
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| Keywords: | Starlike mappings Spirallike mappings Extension operators |
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