Schwarz’s Lemma for Slice Clifford Analysis

It is known that the Schwarz lemma in Clifford analysis does not hold at least in the original form. In this article we find that the situation in slice Clifford analysis is totally different. The sharp Schwarz lemma in slice Clifford analysis holds true in the original form, as well as the Cartan theorem, the Hopf lemma, and the Burns-Krantz theorem. The point of these theorems in slice Clifford analysis is that the results hold for such a map f:Rm+1→R0,m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f :\mathbb{R}^{m+1} \rightarrow \mathbb{R}_0,m}$$\end{document} that is not a self map for any m ≥ 2.