Interior Holder estimate for the linearized complex Monge-Ampere equation

Let w(0) be a bounded, C-3, strictly plurisubharmonic function defined on B-1 subset of Cn. Then w(0) has a neighborhood in L-infinity (B-1). Suppose that we have a function phi in this neighborhood with 1 - epsilon <= MA(phi) <= 1 + epsilon and there exists a function u solving the linearized complex Monge-Ampere equation: det(phi(kl)) phi(ij)u(ij) = 0. Then there exist constants alpha > 0 and C such that vertical bar u vertical bar C-alpha(B-1/2 (0)) <= C, where alpha > 0 depends on n and C depends on n and vertical bar u vertical bar(L infinity (B1(0))), as long as epsilon is small depending on n. This partially generalizes Caffarelli-Gutierrez's estimate for linearized real Monge-Ampere equation to the complex version.