AI 中文总结
该研究针对多复变量的单位多圆盘上的有界全纯函数，建立并改进了含欧拉算子、面积泛函的尖锐玻尔不等式，将相关结果推广至多维情形并证明其尖锐性。
AI 中文摘要
本文建立了$\boldsymbol{\textit{C}}^n$中映射到单位多圆盘$\boldsymbol{\textit{P}\boldsymbol{\bigtriangleup}(0;1_n)}$的有界全纯函数的几类高维改进型玻尔不等式的推广。首先，我们结合平方系数项和面积泛函分量，构造了Liu等人[《Bull. Sci. Math.》第173卷（2021年），第103054页]最初建立的尖锐型玻尔不等式的多维类似形式；其次，我们通过引入对应面积泛函的类似项，为Ahamed等人[《Complex Anal. Oper. Theory》第20卷第6期（2026年），第142页]近期提出的多维扩展结果提供了改进的不等式；最后，我们将含$\boldsymbol{\textit{|f(z)-a}_0\boldsymbol{|}}$项的改进型玻尔不等式推广到多复变量情形。所有结果均被证明是尖锐的。
英文摘要
In this paper, we establish several higher-dimensional generalizations of refined Bohr-type inequalities for bounded holomorphic functions mapping into the unit polydisk $\mathbb{P}Δ(0;1_n)$ in $\mathbb{C}^n$. First, we formulate multidimensional analogues of sharp Bohr-type inequalities originally established by Liu \emph{et al.} [{\it Bull. Sci. Math.} {\bf 173} (2021) 103054], incorporating both squared coefficient terms and area functional components. Second, we provide improved inequalities for a recent multidimensional extension by Ahamed \emph{et al.} [{\it Complex Anal. Oper. Theory} {\bf 20}(6) (2026), 142] by introducing an analogous term corresponding to the area functional. Finally, we extend a refined Bohr-type inequality involving the term $\vert{}f(z)-a_0\vert{}$ to the setting of several complex variables. All the results are shown to be sharp.
Comments18 pages
