A new plurisubharmonic capacity and functions holomorphic along holomorphic vector fields

The main purpose of this article is to present a generalization of Forelli’s theorem for functions holomorphic along a suspension of integral curves of a diagonalizable vector field of aligned type. For this purpose, we develop a new capacity theory that generalizes the theory of projective capacity introduced by Siciak \cite{Siciak82}. Our main theorem improves the results of \cite{KPS09}, \cite{Cho22} as well as the original Forelli’s theorem.