两类双全纯映照子族在Roper-Suffridge延拓算子下的不变性

The Invariance of Two Subclasses of Biholomorphic Mappings Under the Roper-Suffridge Extension Operators

该文将已有的Roper-Suffridge延拓算子在Bergman-Hartogs域上进行了推广,应用α次β型螺形映照及复数λ阶殆星映照的几何性质及增长定理,讨论了推广后的RoperSuffridge延拓算子在Bergman-Hartogs域上保持α次β型螺形性及复数λ阶殆星性,并得到一些特殊情况.所得结论为构造多复空间中的α次β型螺形映照及复数λ阶殆星映照提供了新的途径.

In this paper, we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Applying the geometric properties and the growth theorems of spirallike mappings of type β and order α as well as almost starlike mappings of complex order λ, we obtain that the generalized Roper-Suffridge operators preserve spirallikeness of type β and order α as well as almost starlikeness of complex order λ on Bergman-Hartogs domains which lead to some special cases. The conclusions provide new approaches to construct spirallike mappings of type β and order α and almost starlike mappings of complex order λ in several complex variables.