AI 中文总结
研究单位多圆盘上一类由二阶偏导数和特定界定义的归一化多重调和映射$\mathcal{P}_{\mathcal{H}_n^0}(M)$，通过证明与全纯函数类的对应关系，给出其函数的精确系数界和增长估计。
AI 中文摘要
本文首先引入并研究了归一化多重调和映射类$\mathcal{P}_{\mathcal{H}_n^0}(M)$，其特征是二阶偏导数之和有特定界。证明了该多重调和类与一类全纯函数之间的一一对应关系，将已知结果推广到多复变情形。最后给出了$\mathcal{P}_{\mathcal{H}_n^0}(M)$类函数的精确系数界和增长估计。
英文摘要
In this paper, we first introduce and study the class $\mathcal{P}_{\mathcal{H}_n^0}(M)$ of normalized pluriharmonic mappings, characterized by a specific bound on the sum of their second-order partial derivatives. We prove a one-to-one correspondence between this pluriharmonic class and a class of holomorphic functions, extending the known result of Ghosh and Vasudevarao \cite{Ghosh-Allu-2020} to the setting of several complex variables. Finally, we provide sharp coefficient bounds and growth estimates for functions in the class $\mathcal{P}_{\mathcal{H}_n^0}(M)$.
