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Improved and Refined Bohr-Type Inequalities for Slice Regular Functions over Octonions (2507.01981v1)

Published 26 Jun 2025 in math.CV

Abstract: 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.

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