The ${\mathcal{C}}^{2,\alpha }$ estimate of complex Monge-Ampere equation

We prove that any ${\mathcal{C}}^{1,1}$ solution to complex Monge-Amp`ere equation $det(u_{i\bar{j}})=f$ with $0<f\in {\mathcal{C}}^{\alpha }$ is in ${\mathcal{C}}^{2,\alpha }$ for $\alpha\in (0,1)$.