Bohr theorems for slice regular functions over octonions

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.

On the fourth and fifth coefficients in the Carathéodory class

In the paper, we give general parametric formulas for the fourth and fifth coefficients of functions in the Carath?odory class.