H\'older continuous solutions of the Monge-Amp\`ere equation on compact Hermitian manifolds

We show that a positive Borel measure of positive finite total mass, on compact Hermitian manifolds, admits a Holder continuous quasi-plurisubharmonic solution to the Monge-Ampere equation if and only if it is dominated locally by Monge-Ampere measures of Holder continuous plurisubharmonic functions.
Comment: 11 pages. Final version to appear in Ann. Inst. Fourier