The Complex Monge-Ampère Equation in the Cegrell’s Classes

In this paper, we give some local characterizations of existence of solutions of the complex Monge–Ampère equation in the classes \(\mathcal {E}_\chi (\Omega )\) ${\mathcal{E}}_{\chi }(\mathrm{\Omega })$ and \(\mathcal {E}_{\chi ,loc}(\Omega )\) ${\mathcal{E}}_{\chi ,loc}(\mathrm{\Omega })$ .