(Corollary 5.2) Let $\varphi$ be a smooth solution to (1.1), (1.2), then for any $1<p<\infty$, there exists a constant $C$, depending only on the background Kähler metric $(M,g)$, an upper bound of $\int_{M}e^{F}Fdvol_{g}$, and $p$, such that