The Complex Monge–Ampère Operator on Bounded Domains in ${\mathbb{C}^{n}}$

Abstract.

The aim of the present paper is to establish the inequality of Xing’s type for the class ${\mathcal{D}}$ introduced and investigated by [7] in recent time. Some properties of the class of ${\mathcal{D}}$ is given. The weak continuity of the Monge–Ampère on the class ${\mathcal{B}_{loc}}$ is considered. Finally we give some results on the range of the Monge–Ampère operator in the class ${\mathcal{D}^{u,a}}$ and ${\mathcal{B}^{u,a}_{loc}}$.