We study the relation between simply and universally interpolating sequences for the holomorphic Hardy spaces \(H^p(\mathbb {D}^d)\) 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 \(d\ge 2\) , Amar showed that Shapiro and Shields’ theorem holds for \(H^p(\mathbb {D}^d)\) when \(p \ge 4\) . In contrast, we show that if \(1\le p \le 2\) there exist simply interpolating sequences which are not universally interpolating.
