A New Plurisubharmonic Capacity and Functions Holomorphic Along Holomorphic Vector Fields

The main purpose of this article is to present a generalization Forelli’s theorem for functions holomorphic along suspension integral curves diagonalizable vector field aligned type. For purpose, we develop new capacity theory that generalizes the projective introduced by Siciak (Sophia Kokyuroku Math 14:1–96, 1982). Our improves results Kim et al. (J Geom Anal 19(3):655–666, 2009) and Cho (Complex Var. Elliptic Equ., 2022) as well original theorem.