Simply interpolating and Carleson sequences for Hardy spaces in the polydisc

Abstract

Abstract We study the relation between simply and universally interpolating sequences for the holomorphic Hardy spaces H p(Dd ) on the polydisc. In dimension d = 1 a sequence is simply interpolating if and only if it is universally interpolating, due to a classical theorem of Shapiro and Shields. In dimension d ≥ 2, Amar showed that Shapiro and Shields’ theorem holds for H p(Dd ) when p ≥ 4. In contrast, we show that if 1 ≤ p ≤ 2 there exist simply interpolating sequences which are not universally interpolating.