Note on a general complex Monge-Ampère equation on pseudoconvex domains of infinite type

Let [OMEGA] be a smoothly bounded domain in [C.sup.n], for n [greater than or equal to] 2. For a given continuous function [phi] on b[OMEGA], and a non-negative continuous function [PSI] on R x [OMEGA], the main purpose of this note is to seek a plurisubharmonic function u on [OMEGA], continuous on [OMEGA], which solves the following Dirichlet problem of the complex Monge-Ampere equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] In particular, the boundary regularity for the solution of this complex, fully nonlinear equation is studied when [OMEGA] belongs to a large class of weakly pseudoconvex domains of finite and infinite type in [C.sup.n]. Key words: Pseudoconvexity; D'Angelo type; complex Monge-Ampere operator; Perron Bremermann family.