C^n中单位多圆柱上一类α次星形映照第四项齐次展开式的精确估计

The Sharp Estimate of the Fourth Homogeneous Expansion for a Class of Starlike Mappings of Orderαon the Unit Polydisk in C^n

主要在Cn中单位多圆柱上建立一类α次星形映照第四项齐次展开式的精确估计,所得结论是已有结果的进一步深化,且显示在一定的限制条件下,多复变数中关于α次星形映照第四项齐次展开式的Bieberbach猜想成立.

We mainly obtain the sharp estimate of the fourth homogeneous expansion for a class of nor-malized Biholomorphic starlike mappings defined on the unit polydisk inCn .Our result deepens the known result in several complex variables,and it is shown that the Bieberbach conjecture concerning the fourth homogeneous expansion for starlike mappings of orderα in several complex variables under the restricted condition holds.