AI 中文总结
该研究在多复变量框架下引入正则化多重调和映射类，建立其精确系数估计与增长定理，确定Bohr半径并研究函数截面，推广了已有结果。
AI 中文摘要
我们在多复变量框架下引入了一类正则化多重调和映射类$\boldsymbol{\text{℘}}_{\boldsymbol{\text{ℋ}}_n^0}(\boldsymbol{\boldsymbol{\text{α}}})$（其中$0 \boldsymbol{\boldsymbol{\text{≤}}} \boldsymbol{\boldsymbol{\text{α}}} \boldsymbol{\boldsymbol{\text{<}}} \boldsymbol{\boldsymbol{\text{1}}}$），该类将调和映射族$\boldsymbol{\text{℘}}_{\boldsymbol{\text{ℋ}}}^{0}(\boldsymbol{\boldsymbol{\text{α}}})$拓展到了多维情形。我们对$\boldsymbol{\text{℘}}_{\boldsymbol{\text{ℋ}}_n^0}(\boldsymbol{\boldsymbol{\text{α}}})$中的函数建立了精确的系数估计和增长定理，从而推广了Li和Ponnusamy（2013a）以及Allu和Halder（2021）的相应结果。我们还确定了相关的Bohr半径，并研究了该类函数的截面（部分和），获得了描述其截断展开行为的定量结果。
英文摘要
We introduce the class $\mathscr{P}_{\mathcal{H}_n^0}(α)$ $(0\leq α<1)$ of normalized pluriharmonic mappings in the setting of several complex variables. This class extends the harmonic family $\mathscr{P}_{\mathcal{H}}^{0}(α)$ to the multidimensional framework. We establish sharp coefficient estimates and growth theorems for functions in $\mathscr{P}_{\mathcal{H}_n^0}(α)$, thereby generalizing the corresponding results of Li and Ponnusamy \cite{Li-Ponnusamy-2013a} and Allu and Halder \cite{Allu-Halder-2021}. We further determine the associated Bohr radius and investigate the sections (partial sums) of functions in this class, obtaining quantitative results that describe the behavior of their truncated expansions.
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