Holder continuity of solutions to the complex Monge-Ampere equations on compact Kahler manifolds

We study H\"older continuity of solutions to the Monge-Amp\`{e}re equations on compact K\"ahler manifolds. In [DNS] the authors have shown that the measure $\omega_u^n$ is moderate if $u$ is H\"older continuous. We prove a theorem which is a partial converse to this result.