| 崔艳艳,刘浩.Hartogs域上延拓算子的性质[J].数学年刊A辑,2019,40(2):139~156 |
| Hartogs域上延拓算子的性质 |
| Properties of the Perturbed Extension Operators on Hartogs Domains |
| Received:May 08, 2017 Revised:August 19, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0012 |
| 中文关键词: Starlike mappings, Spirallike mappings, Extension operators, |
| 英文关键词:Starlike mappings, Spirallike mappings, Extension operators, |
| 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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| 中文摘要: |
| 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$\Omega_N$上保持强$\alpha$次殆$\beta$型螺形映照、$\alpha$次殆$\beta$型螺形映照和
$\alpha$次$\beta$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$\mathbb{C}^n$中的双全纯映照提供了新的途径. |
| 英文摘要: |
| This paper mainly discuss the properties of the generalized Roper-Suffridge
operators on the extended Hartogs domains. By using the distortion
results of subclasses of biholomorphic mappings, the authors conclude that
the generalized operators preserve the properties of strong and
almost 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 the
corresponding results on $B^n$. These conclusions involve some known
results and provide new approaches to research the biholomorphic
mappings in $\mathbb{C}^n$. |
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