Growth theorems in slice analysis of several variables

TL;DR

This paper introduces a class of slice mappings in several Clifford variables and establishes growth theorems for slice regular starlike or convex mappings on specific domains, advancing the understanding of slice analysis in multiple variables.

Contribution

It defines new slice mappings in Clifford analysis and proves growth theorems for slice regular functions on various domains, extending classical results to several variables.

Findings

Established growth theorems for slice regular starlike mappings

Proved growth bounds for convex slice regular mappings

Extended slice analysis results to multiple variables and domains

Abstract

In this paper, we define a class of slice mappings of several Clifford variables, and the corresponding slice regular mappings. Furthermore, we establish the growth theorem for slice regular starlike or convex mappings on the unit ball of several slice Clifford variables, as well as on the bounded slice domain which is slice starlike and slice circular.