Let $${D_{{p_1},{p_2}, \cdots ,{p_n}}} = {\rm{\{ }}z \in {\mathbb{C}^n}{\rm{:}}\sum\limits_{l = 1}^n {{{\left| {{z_l}} \right|}^{{p_l}}} 1,l = 1,2, \cdots \;,n}.$$ . In this article, we first establish the sharp estimates of the main coefficients for a subclass of quasi-convex mappings (including quasi-convex mappings of type $$\mathbb{A}$$ and quasi-convex mappings of type $$\mathbb{B}$$ ) on $${D_{{p_1},{p_2}, \cdots ,{p_n}}}$$ under some weak additional assumptions. Meanwhile, we also establish the sharp distortion theorems for the above mappings. The results that we obtain reduce to the corresponding classical results in one dimension.

中文翻译：

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ℂn 中 Reinhardt 域上的拟凸映射的子类

让 $${D_{{p_1},{p_2}, \cdots ,{p_n}}} = {\rm{\{ }}z \in {\mathbb{C}^n}{\rm{:}} \sum\limits_{l = 1}^n {{{\left| {{z_l}} \right|}^{{p_l}}} 1,l = 1,2, \cdots \;,n}.$$ 。在本文中，我们首先建立了准凸映射子类（包括 $$\mathbb{A}$$ 类型的准凸映射和 $$\mathbb 类型的准凸映射）的主要系数的尖锐估计{B}$$ ) 在 $${D_{{p_1},{p_2}, \cdots ,{p_n}}}$$ 上的一些弱附加假设。同时，我们还建立了上述映射的尖锐失真定理。我们得到的结果在一维上简化为相应的经典结果。