两类螺形映照扩充子族的偏差上界估计

偏差估计一直是多复变函数论的研究热点之一.但目前螺形映照扩充子族的偏差估计的研究成果还较少.针对这一问题,研究了复向量空间C_n中开单位球B_n,复Banach空间中单位球B和域Ω_(p_1,…,p_n)上一类α次β型,α次强β型螺形映照的偏差估计问题.利用不等式、矩阵及两类映照的增长定理等方法,获得了上述域上的两种映照的偏差上界估计,所得结果推广了一些已知的结论.

The Distortion Upper Bound for Two Subclasses of Spirallike Mappings

Distortion estimations have been one of the focuses of the theory of several complex variables functions,But now the distortion estimations on some subclasses of spirallike mappings are less.Aiming this issue,This paper researched the distortion estimation of almost spirallike mapping of β and order a,strongly spirallike mapping of type β and order α on unit ball B_n in complex vector space C_n,unit ball B on complex Banach space and reinhard domain Ω_(p1,...pn).By using the methods such as inequality,matrix and the growth and cover theorem of two classes spirallike mapping,we obtained the distortion upper bound on above several domains,and the results gerenalized some known conclusions.