In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous e...In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cnare also obtained. Our results show that a weak version of the Bieberbach conjecture in several complex variables is proved, and the obtained conclusions reduce to the classical results in one complex variable.展开更多
基金supported by Key Program of National Natural Science Foundation of China(Grant No.11031008)National Natural Science Foundation of China(Grant No.11061015)
文摘In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cnare also obtained. Our results show that a weak version of the Bieberbach conjecture in several complex variables is proved, and the obtained conclusions reduce to the classical results in one complex variable.
