Abstract: summary:We prove, among other results, that $\min (u,v)$ is plurisubharmonic (psh) when $u,v$ belong to a family of functions in ${\rm psh}(D)\cap \Lambda _{\alpha }(D),$ where $\Lambda _{\alpha }(D)$ is the $\alpha $-Lipchitz functional space with $1<\alpha <2.$ Then we establish a new characterization of holomorphic functions defined on open sets of $\mathbb {C}^n.$
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