AI 中文总结
研究单位多圆盘上归一化多重调和映射的\(\mathcal{W}_{\mathcal{H}_n^0}(\alpha)\)类，通过建立与全纯函数类的对应扩展相关结果，还得到该类函数的系数界、增长估计等，且引入并研究了其截面的性质。
AI 中文摘要
本文引入并研究了归一化多重调和映射的\(\mathcal{W}_{\mathcal{H}_n^0}(\alpha)\)类，其由二阶偏导数的适当界来刻画。我们建立了这个多重调和类与一类相关全纯函数之间的一一对应，从而将Ghosh和Vasudevarao的结果扩展到多复变情形。此外，我们得到了\(\mathcal{W}_{\mathcal{H}_n^0}(\alpha)\)中函数的精确系数界、增长估计和凸组合定理。最后，我们引入多重调和映射的截面（部分和）并研究其对于\(\mathcal{W}_{\mathcal{H}_n^0}(\alpha)\)中函数的性质。
英文摘要
In this paper, we introduce and study the class $\mathcal{W}_{\mathcal{H}_n^0}(α)$ of normalized pluriharmonic mappings, characterized by a suitable bound on their second-order partial derivatives. We establish a one-to-one correspondence between this pluriharmonic class and an associated class of holomorphic functions, thereby extending a result of Ghosh and Vasudevarao \cite{Ghosh-Allu-2019} to the setting of several complex variables. Furthermore, we obtain sharp coefficient bounds, growth estimates and a convex combination theorem for functions in $\mathcal{W}_{\mathcal{H}_n^0}(α)$. Finally, we introduce sections (partial sums) of pluriharmonic mappings and investigate their properties for functions belonging to $\mathcal{W}_{\mathcal{H}_n^0}(α)$.
