In this paper, we mainly investigate two versions of the Bohr theorem for slice regular functions over the largest alternative division algebras of octonions $\mathbb {O}$. To this end, we establish the coefficient estimates for self-maps of the unit ball of $\mathbb {O}$ and the Carathéodory class in this setting. As a further application of the coefficient estimate, the 1/2-covering theorem is also proven for slice regular functions with convex image.

中文翻译：

---

八元数上切片正则函数的玻尔定理

在本文中，我们主要研究了两个版本的玻尔定理，用于在最大的八元数替代除法代数上的切片正则函数$\mathbb {O}$. 为此，我们建立了单位球自映射的系数估计。$\mathbb {O}$和此设置中的 Carathéodory 课程。作为系数估计的进一步应用，1/2覆盖定理也被证明适用于具有凸图像的切片规则函数。