Reinhardt域上的双全纯映照与Roper-Suffridge算子

Biholomorphic Mappings on Reinhardt Domains and Generalized Roper-Suffridge Operators

讨论了推广的Roper-Suffridge算子保持双全纯映照子族的性质,从全纯函数的最大模原理及定义出发证明了推广的Roper-Suffridge算子在有界完全Reinhardt域Ω_(n,p2,…,pn)上保持S_Ω~*(β,A,B)及强α次殆β型螺形映照的性质,进而得到推广的Roper-Suffridge算子在相应的域上分别保持S_Ω~*(A,B)、α次星形性、α次强星形性以及强α次殆星形性、强β型螺形性.

The generalized Roper-Suffridge operators＆#39; preserving the properties of subclasses of biholomorphic mappings were discussed.With the maximum modulus principle and the definitions for holomorphic functions, the generalized operators were proved to preserve the properties of S＊Ω（β,A,B）, strong and almost spirallike mappings of type β and order α on Ωn,p2,…,pn.And some generalized operators were proved to keep respectively S＊Ω（A,B）, starlikeness of order α, strong starlikeness of order α, strong and almost starlikeness of order α, strong spirallikeness of type β on the corresponding domains.