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

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 ${\mathbb{H}}^2$.