We prove, among other results, that min(u, v) is plurisubharmonic (psh) when u, v belong to a family of functions in psh(D) ∩ Λα(D), where Λα(D) is the α-Lipchitz functional space with 1 < α < 2. Then we establish a new characterization of holomorphic functions defined on open sets of ℂ n .