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

TL;DR

This paper investigates the relationship between Carleson measures and $H^{p}$ interpolating sequences in the polydisc, establishing conditions under which sequences are Carleson and providing criteria for interpolation.

Contribution

It proves that $H^{p}$ interpolating sequences are Carleson in the polydisc for $p>2$ and offers a new sufficient condition involving dual boundedness and Carleson measures.

Findings

$H^{p}$ interpolating sequences are Carleson for $p>2$

A new sufficient condition for $H^{p}$ interpolation involving dual boundedness

Characterization of $H^{p}$ 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.