Let $\Omega\subset \mathbb{C}^n$ be an open subset. Let $u\colon \Omega\to [-\infty,+\infty)$ be an upper semi-continuous function.

Recall that $u$ is called plurisubharmonic (psh) if its restriction to any complex line is subharmonic.

Any psh function $u$ satisfies the following property: for any point $x\in \Omega$ and for any $C^2$-smooth function $\phi$ defined near $x$ and such that $u\leq \phi$ and $u(x)=\phi(x)$ one has $$(\Delta_L (\phi|_L))(x)\geq 0$$ for any complex line $L$ containing the point $x$. Here $\Delta_L$ denotes the Laplacian on the line $L$.

**Is the converse true, i.e. if an upper semi-continuous function $u$ satisfies the above condition is it psh? A reference would be very helpful.**

This post is a continuation of A possible characterization of subharmonic functions