复Banach空间单位球上一类星形映照子族齐次展开式的精确估计

The Sharp Estimates of the Homogeneous Expansions for a Subclass of Starlike Mappings on the Unit Ball of a Complex Banach Space

本文建立了复Banach空间的单位球上一类星形映照子族第三项、第四项及第五项齐次展开式的精确估计,所得结果能回到单复变数的经典结论,从而丰富了多复变数Bieberbach猜想的研究.

In this paper, the sharp estimates of the third, fourth and fifth homogeneous expansions for a subclass of starlike mappings on the unit ball of a complex Banach space are established, and the results can reduce to the classical conclusion of one complex variables. Hence, the study of Bieberbach conjecture of several complex variables are enriched.