多复变数某类推广的螺型映射精确的系数估计

The Sharp Coefficient Estimates for a Certain General Class of Spirallike Mappings in Several Complex Variables

主要用统一方法建立限制条件下复Banach空间单位球与Cn中单位多圆柱上某类推广的β型螺型映射全部项齐次展开式的精细估计.同时,也用统一方法建立较弱限制条件下C^(n)中Dp1,p2,…,pn=■,pl>1,l=1,2,…,n上某类推广的β型螺型映射主要系数的精细估计.特别地,限制条件下k折对称β型螺型映射的结果是精确的.所得结果包含前面文献中许多已知结论.

In this article,the author chiefy establishes the refined estimates of all homogeneous expansions for a certain general class of spirallike mappings of typeβon the unit ball in complex Banach spaces and the unit polydisk in Cn under restricted conditions with a unified method.Meanwhile,the author obtains the refined estimates of main coeficient for a certain general class of spirlike mappings of type■Cn under weaker restricted conditions with a unified method as well.In particular,the results are sharp for k-fold symmetric spirallike mapping of typeβunder additional assumptions.The derived results include many known results in the prior references.