Subharmonicity and a Version of Riesz Theorem on Harmonic Conjugates

The aim of the paper is to prove a monogenic version of classical M. Riesz theorem on harmonic conjugates in the framework of quaternionic analysis in R4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{4}}$$\end{document}. Our proof is subharmonic and somewhat simpler than that for less general Riesz-Stein-Weiss systems of harmonic conjugate functions.