Weighted composition operators on de Branges-Rovnyak spaces

In this paper, we characterize the boundedness and the compactness of weighted composition operators acting on a de Branges-Rovnyak space $\mathcal{H}(b)$, where the symbol $b$ is a rational function in the unit ball of $H^{\mathrm{\infty }}$ that is not a finite Blaschke product. Our results extend those of [2] by exploiting a close relationship between weighted composition operators on $\mathcal{H}(b)$ and their counterparts on the Hardy space $H^2$.