Some remarks on the Cegrell's class $\mathcal{F}$

In this paper, we study the near-boundary behavior of functions $u\in \mathcal{F}(\mathrm{\Omega })$ in the case where $\mathrm{\Omega }$ is strictly pseudoconvex. We also introduce a sufficient condition for belonging to $\mathcal{F}$ in the case where $\mathrm{\Omega }$ is the unit ball.