  In this note, we obtain a full characterization of radial Carleson measures
for the Hilbert-Hardy space on tube domains over symmetric cones. For large
derivatives, we also obtain a full characterization of the measures for which
the corresponding embedding operator is continuous. Restricting to the case of
light cones of dimension three, we prove that by freezing one or two variables,
the problem of embedding derivatives of the Hilbert-Hardy space into Lebesgue
spaces reduces to the characterization of Carleson measures for Hilbert-Bergman
spaces of the upper-half plane or the product of two upper-half planes.
