ABSTRACT

Let $D_{p_1,p_2,\dots ,p_n}=\{z\in {\mathbb{C}}^n:\sum _{j=1}^n|z_j{|}^{p_j}<1\},p_j>1,j=1,2,\dots ,n$. We mainly establish the sharp estimates of main coefficients of all homogeneous expansions for starlike mappings and starlike mappings of order α on $D_{p_1,p_2,\dots ,p_n}$ under some weak restricted conditions. Our derived results are the generalization of the corresponding classical results in one complex variable.

中文翻译：

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ℂn 中星状映射的主要系数的尖锐估计

摘要

让 $D_{{磷}_1,{磷}_2,\dots ,{磷}_n}=\{z\in {\mathbb{C}}^n：\sum _{j=1}^n|z_j{|}^{{磷}_j}<1\},{磷}_j>1,j=1,2,\dots ,n$. 我们主要建立星形映照所有均质扩张的主要系数急剧估计和星象秩序的映射α上$D_{{磷}_1,{磷}_2,\dots ,{磷}_n}$在一些弱限制条件下。我们得出的结果是在一个复杂变量中相应经典结果的推广。