ON PLURIHARMONICITY CRITERIA OF HARMONIC AND \(\mathcal M\)-HARMONIC FUNCTIONS IN THE ARBITRARY BALL OF \({\mathbb C}^{n}\)

This paper introduces the concept of \({\mathcal M}\)-harmonic function in an arbitrary ball of \({\mathbb C}^{n}\) and proves some criteria for pluriharmonicity of harmonic functions in this ball. It is devoted to the study of the connection between the invariant Laplacian and the specificity of the domain and for this purpose we will try to define the invariant Laplacian for arbitrary ball of \({\mathbb C}^{n}\)$. Moreover, we will give the criteria for pluriharmonicity in terms of \({\mathcal M}\)-harmonicity with respect to two different balls. The main goal of this work is expanding the properties of pluriharmonic functions furthermore and study their connection with harmonic and \({\mathcal M}\)-subharmonic functions.

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