Maximal subextension of $m$-subharmonic functions

In this paper, we prove that given a quasi-$m$-hyperconvex domain $Ω\subset X$ in a compact Kähler manifold $(X, ω)$, and a function $φ$ in the weighted energy class $\mathcal{E}_χ^m(Ω, ω)$ with respect to a convex weight function $χ: \mathbb{R} \to \mathbb{R}$, then there exists a maximal $ω$-$m$-s