  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 $\Omega$ of $\Bbb C^n$. We
introduce two classes $\mathcal{F}_{p}^{T}(\Omega)$ and
$\mathcal{E}_p^T(\Omega)$ 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.
