Solutions of the complex Monge-Ampère Equation are obtained in the Sobolev topology on complex manifolds and through the Delta-Delta-Bar Lemma, in case the manifold is compact Kähler, a simple proof is given of the Aubin-Calabi-Yau Theorem.
"Sobolev Estimates for the Complex Monge-Ampère Operator on Complex Manifolds." Afr. Diaspora J. Math. (N.S.) 16 (1) 55 - 58, 2013.