On the Cegrell Classes Associated to a Positive Closed Current

Abstract

The aim of this paper is to study the operator (dd ^c▪) ^q ∧ T on some classes of plurisubharmonic (psh) functions, which are not necessary bounded, where T is a positive closed current of bidimension (q, q) on an open set Ω of ℂ ⁿ. The author introduces two classes ${\cal F}_p^T\left( {\rm{\Omega }} \right)$ and ${\cal E}_p^T\left( {\rm{\Omega }} \right)$ and shows first that they belong to the domain of definition of the operator (dd ^c▪) ^q ∧ T. Then the author proves that all functions that belong to these classes are C _T-quasi-continuous and that the comparison principle is valid for them.

Keywords

Positive closed current / Plurisubharmonic function / Capacity / Monge-Ampère Operator