多复变数某类推广的螺型映射精确的系数估计

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Cn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.

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

In this article, the author chiefly establishes the refined estimates of all homogeneous expansions for a certain general class of spirallike mappings of type $\beta$ on the unit ball in complex Banach spaces and the unit polydisk in $\mathbb{C}^n$ under restricted conditions with a unified method. Meanwhile, the author obtains the refined estimates of main coefficient for a certain general class of spirallike mappings of type $\beta$ on $D_{p_1,p_2,\cdots,p_n}=\big\{z\in \mathbb{C}^n: \sum\limits_{l=1}^n|z_l|^{p_l}<1\big\}, p_l>1, l=1,2,\cdots,n$ on $\mathbb{C}^n$ under weaker restricted conditions with a unified method as well. In particular, the results are sharp for $k$-fold symmetric spirallike mapping of type $\beta$ under additional assumptions. The derived results include many known results in the prior references.