B^n上推广的Roper-Suffridge算子的性质  

Property of the Modified Roper-Suffridge Extension Operators on B^n

作　　者：王朝君[1] 崔艳艳[1] 刘浩[2] 

机构地区：[1]周口师范学院数学与统计学院,周口466001 [2]河南大学数学与统计学院,开封475001

出　　处：《数学学报（中文版）》2016年第6期729-744,共16页Acta Mathematica Sinica：Chinese Series

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)

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、α次β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.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 almostspirallikeness of order α and type β, spirallikeness of order α and type β, strong spiral- likeness of type fl on Bn, respectively. Sequentially, we get that the modified Roper- Suffridge operators preserve almost starlikeness of orderα, starlikeness of order α and strong starlikeness on Bn. The conclusions provide a new approach to construct these biholomorphie mappings in several complex variables.

关 键 词：Roper-Suffridge延拓算子 螺形映照 星形映照 

分 类 号：O174.56[理学—数学]