F. Forelli-type theorems for dense directions in the unit ball

In this paper, we establish sufficient conditions for the pluriharmonicity of real-valued functions defined in the unit ball in $\mathbb{C}^n$. Our main result generalizes the classical form of Forelli’s theorem by replacing the requirement of harmonicity along all radial directions with the requirement of harmonicity along a dense subset of directions on the sphere. This approach significantly broadens the scope of applicability of Forelli-type results. On this basis, the relationship between $M$-harmonicity and pluriharmonicity is also analyzed.

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