Hartogs域上延拓算子的性质

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Ω_N上保持强α次殆β型螺形映照、α次殆β型螺形映照和α次β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C~n中的双全纯映照提供了新的途径.

Properties of the Perturbed Extension Operators on Hartogs Domains

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 $\mathbb{C}^n$.