标题： 改进和细化八元数上分片正则函数的博尔类型不等式 显示英文标题

标题： Improved and Refined Bohr-Type Inequalities for Slice Regular Functions over Octonions

摘要： 四元数函数理论到八元数的一个关键扩展是切片正则函数的概念，该概念被引入以在非结合设置中处理类似全纯的性质。 在本文中，首先我们提出了博尔不等式的推广，并改进了在最大替代除法代数八元数$\mathbb{O}$上的切片正则函数的博尔不等式。 此外，我们提供了在$\mathbb{B}$上的切片正则函数$f$的博尔不等式的精化版本，使得对于所有$x \in \mathbb{B}$都有$ {\rm Re}(f(x)) \leq 1 $。 所有结果都被证明是精确的。 显示英文摘要

摘要： A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative setting. In this paper, first we present a generalization of the Bohr inequality, and improved versions of the Bohr inequality for slice regular functions over the largest alternative division algebras of octonions $\mathbb{O}$. Moreover, we provide a refined version of the Bohr inequality for slice regular functions $f$ on $\mathbb{B}$ such that $ {\rm Re}(f(x)) \leq 1 $ for all $x \in \mathbb{B}$. All the results are shown to be sharp.