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Bohr theorems for slice regular functions over octonions

Part of: Geometric function theory General nonassociative rings Generalized function theory

Published online by Cambridge University Press:  21 October 2020

Zhenghua Xu
Zhenghua Xu*
Affiliation:
School of Mathematics, HeFei University of Technology, Hefei230601, China (zhxu@hfut.edu.cn)
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Abstract

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.

Keywords

function of one hypercomplex variabledivision algebrasBohr theoremcovering theorem

MSC classification

Primary: 30G35: Functions of hypercomplex variables and generalized variables
Secondary: 17A35: Division algebras 30C25: Covering theorems in conformal mapping theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 5 , October 2021 , pp. 1595 - 1610
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Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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