A Liouville-type theorem on halfspaces for the Kohn Laplacian

Let $\Delta _{ \mathbb{H}^{n}}$ be the Kohn Laplacian on the Heisenberg group $\mathbb{H}^{n}$ and let $\Omega$ be a halfspace of $\mathbb{H}^{n}$ whose boundary is parallel to the center of $\mathbb{H}^{n}$. In this paper we prove that if $u$ is a non-negative $\Delta _{ \mathbb{H}^{n}}$-superharmonic function such that

then $u\equiv 0$ in $\Omega$.