Carleson measures and $H^p$ interpolating sequences in the polydisc

Let $S$ be a sequence of points in ${\mathbb{D}}^n\mathrm{.}$ Suppose that $S$ is $H^p$ interpolating. Then we prove that the sequence $S$ is Carleson, provided that $p>2.$ We also give a sufficient condition, in terms of dual boundedness and Carleson measure, for $S$ to be an $H^p$ interpolating sequence.