Carleson and sampling measures on Bernstein spaces on Siegel CR manifolds

In this paper, we introduce and study Carleson and sampling measures on Bernstein spaces on a class of quadratic CR manifold called Siegel CR manifolds. These are spaces of entire functions of exponential type whose restrictions to the given Siegel CR manifold are $L^p$-integrable with respect to a natural measure. For these spaces, we prove necessary and sufficient conditions for a Radon measure to be a Carleson or a sampling measure. We also provide sufficient conditions for sampling sequences.