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Subharmonicity and a Version of Riesz Theorem on Harmonic Conjugates

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Abstract

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 \({\mathbb{R}^{4}}\). Our proof is subharmonic and somewhat simpler than that for less general Riesz-Stein-Weiss systems of harmonic conjugate functions.

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Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, Yerevan State University, Alex Manoogian St. 1, Yerevan, 0025, Armenia

    Karen Avetisyan

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  1. Karen Avetisyan
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Correspondence to Karen Avetisyan.

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Dedicated to Professor Klaus Gürlebeck on the occasion of his 60th birthday

This paper is partially supported by DAAD, the German Academic Exchange Service.

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Avetisyan, K. Subharmonicity and a Version of Riesz Theorem on Harmonic Conjugates. Adv. Appl. Clifford Algebras 24, 909–919 (2014). https://doi.org/10.1007/s00006-014-0465-1

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  • DOI: https://doi.org/10.1007/s00006-014-0465-1

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