# Some notions of subharmonicity over the quaternions

## TL;DR

This paper introduces new concepts of subharmonic functions for quaternionic variables, connecting them with slice regular functions and constructing quaternionic Green's functions.

## Contribution

It develops several notions of subharmonicity in the quaternionic setting and explores their properties and applications, extending classical potential theory.

## Key findings

- New notions of quaternionic subharmonicity introduced
- Properties of these functions are analyzed and characterized
- Analogues of Green's functions are constructed in the quaternionic context

## Abstract

This works introduces several notions of subharmonicity for real-valued functions of one quaternionic variable. These notions are related to the theory of slice regular quaternionic functions introduced by Gentili and Struppa in 2006. The interesting properties of these new classes of functions are studied and applied to construct the analogs of Green's functions.