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

Abstract

Let $S$ be a sequence of points in ${\mathbb{D}}^n.$ 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.

Due to an terrible mistake I did in the proof of the second main result, thanks to the referee to uncovered it, to get the same result I have to ask for a stronger hypothesis: the measure associated to the sequence must be Carleson and not only square Carleson

Cited by in corpus (1)

• On the linear extension property for interpolating sequences