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

O. I. Omonov

In this paper, we establish sufficient conditions for the pluriharmonicity of real-valued functions defined in the unit ball in Cn. 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. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(1) (2026), pp. 167-175