Theorem 6.3 . [02F9]

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Theorem 6.3.

Let $V$ be a $n$ -dimensional compact normal Kähler space and $\Omega$ be a smooth Kähler form on $V$ . Then for every $f\in L^{p}(V,\Omega^{n})$ , $p>1$ , such that $\int_{V}f\Omega^{n}=\int_{X}\Omega^{n}$ , there is a unique $\varphi\in{\mathcal{C}}^{0}(V)$ such that

(\Omega+dd^{c}\varphi)^{n}=f\Omega^{n}\text{ and }\sup_{V}\varphi=-1.