Pluricomplex energy classes associated to a positive closed current

The aim of this paper is to extend the domain of definition of $(dd^c\centerdot)^q\wedge T$ 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 $\Bbb C^n$. We introduce two classes $\mathcal{F}_{p}^{T}(Ω)$ and $\mathcal{E}_p^T(Ω)$ and we show that they belong to the domain of definition of the operator $(dd^c\centerdot)^q\wedge T$. We also prove that all functions belong to these classes are $C_T$-quasicontinuous and that the comparison principle is valid in them.

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