Let $\phi$ be upper semi-continuous function defined on $\Omega\subset \mathbb C^2$.
Let $\Omega_n= \{z \in \Omega: d(z,\partial \Omega) > \frac1n \}$.
Let $\chi\in C_c^\infty$ of $|z_1|$, $|z_2|$ with support contained in $|z|<1$ satisfying $\chi \geq 0$ and $\int \chi d\zeta\wedge d\bar{\zeta} =1$, and set $\phi_n(z)= \int_{\triangle\times \triangle} \phi\left(z-\frac{\zeta}{n}\right)\chi(\zeta)d\zeta\wedge d\bar{\zeta}$
Notation is index notation: That is $\zeta= (\zeta_1,\zeta_2)$ and same way $z-\zeta$ is also in index notation.
If i understood correctly the below reference, I need to show that $\phi_n$ is $C^\infty $ in $\Omega_n$.
Reference: Giuseppe Zampieri; Complex analysis and CR geometry, Page number 31. You can see the above things clicking the link.. First line in page 31.