Capacity & Perimeter from $alpha$-Hermite Bounded Variation

Let $mathcal{H}_{alpha}=Delta-(alpha-1)|x|^{alpha}$ be an $[1,infty) ialpha$-Hermite operator for the hydrogen atom located at the origin in $mathbb R^d$. In this paper, we are motivated by the classical case $alpha=1$ to investigate the space of functions with $alpha$-{it Hermite Bounded Variation} and its functional capacity and geometrical perimeter.