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function of one hypercomplex variable

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Bohr theorems for slice regular functions over octonions
Part of
Zhenghua Xu
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 5 / October 2021

Published online by Cambridge University Press:

21 October 2020, pp. 1595-1610

Print publication:

October 2021
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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.