Complex Hessian Operator Associated to an m-Positive Closed Current and Weighted m-Capacity

In this paper, we first study the definition and continuity of complex Hessian operator associated to an $m$-positive closed current $T$, for some classes unbounded $m$-subharmonic functions as well when consider a regularization sequence $T$. Next, introduce notion weighted $(m,T)$-capacity in setting investigate link with $m$-extremal function. As application give characterization Cegrell ${\mathscr F}^m$ E}^m$ by means $(m,1)$-capacity. Furthermore, prove subsolution theorem general equation relatively