2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155482We study the complex Monge-Ampère operator in bounded hyperconvex domains of $\C^n$. We introduce a scale of classes of weakly singular plurisubharmonic functions : these are functions of finite weighted Monge-Ampère energy. They generalize the classes introduced by U.Cegrell, and give a stratification of the space of (almost) all unbounded plurisubharmonic functions. We give an interpretation of these classes in terms of the speed of decreasing of the Monge-Ampère capacity of sublevel sets and solve associated complex Monge-Ampère equations.15 pages, dedicated to Christer Kiselman on the occasion of his retirementComplex Variables32W20, 32U05, 32U15text