A half-space theorem for graphs of constant mean curvature 0<H<frac{1}{2} in mathbb{H}²timesmathbb{R}

We study a half-space problem related to graphs in $\mathbb{H}^2\times\mathbb{R}$, where $\mathbb{H}^2$ is the hyperbolic plane, having constant mean curvature $H$ defined over unbounded domains in $\mathbb{H}^2$.