  We show that the complex Monge-Ampere equation on a compact Kaehler manifold
(X,\omega) of dimension n admits a Holder continuous omega-psh solution if and
only if its right-hand side is a positive measure with Holder continuous
super-potential. This property is true in particular when the measure has
locally Holder continuous potentials or when it belongs to the Sobolev space
W^{2n/p-2+epsilon,p}(X) or to the Besov space B^{epsilon-2}_{\infty,\infty}(X)
for some epsilon>0 and p>1.
