Bn上推广的Roper-Suffridge算子的性质

王朝君, 崔艳艳, 刘浩

数学学报 ›› 2016, Vol. 59 ›› Issue (6) : 729-744.

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数学学报 ›› 2016, Vol. 59 ›› Issue (6) : 729-744. DOI: 10.12386/A2016sxxb0065
论文

Bn上推广的Roper-Suffridge算子的性质

    王朝君1, 崔艳艳1, 刘浩2
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Property of the Modified Roper-Suffridge Extension Operators on Bn

    Chao Jun WANG1, Yan Yan CUI1, Hao LIU2
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文章历史 +

摘要

讨论改进后的Roper-Suffridge延拓算子保持双全纯映照子族的性质.借助双全纯映照子族的解析特征及其偏差结论,得到改进后的Roper-Suffridge延拓算子在一定条件下保持α次殆β型螺形映照、αβ型螺形映照、强β型螺形映照的性质,从而得到改进后的算子在一定条件下保持α次殆星形性、α次星形性和强星形性.所得结论为在多复变数空间中构造这些双全纯映照提供了一种新的途径.

Abstract

We mainly discuss the property of the modified Roper-Suffridge operators. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve almost spirallikeness of order α and type β, spirallikeness of order α and type β, strong spiral-likeness of type β on Bn, respectively. Sequentially, we get that the modified Roper-Suffridge operators preserve almost starlikeness of order α, starlikeness of order α and strong starlikeness on Bn. The conclusions provide a new approach to construct these biholomorphic mappings in several complex variables.

关键词

Roper-Suffridge延拓算子 / 螺形映照 / 星形映照

Key words

Roper-Suffridge operator / spirallike mappings / starlike mappings

引用本文

导出引用
王朝君, 崔艳艳, 刘浩. Bn上推广的Roper-Suffridge算子的性质. 数学学报, 2016, 59(6): 729-744 https://doi.org/10.12386/A2016sxxb0065
Chao Jun WANG, Yan Yan CUI, Hao LIU. Property of the Modified Roper-Suffridge Extension Operators on Bn. Acta Mathematica Sinica, Chinese Series, 2016, 59(6): 729-744 https://doi.org/10.12386/A2016sxxb0065

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基金

国家自然科学基金资助项目(U1204618);河南省教育厅科学技术研究重点项目(14B110016)

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