On a Monge–Ampère type equation in the Cegrell class Eχ

Abstract

Let Omega be a bounded hyperconvex domain in C-n and let mu be a positive and finite measure which vanishes on all pluripolar subsets of Omega. We prove that for every continuous and strictly increasing function chi : (-infinity, 0) -> (-infinity, 0) there exists a negative plurisubharmonic function u which solves the Monge-Ampere type equation -chi(u)(dd(c)u)(n) = d mu. Under some additional assumption the solution u is uniquely determined.