On the linear extension property for interpolating sequences

Abstract

Let $S$ be a sequence of points in $\Omega ,$ where $\Omega$ is the unit ball or the unit polydisc in ${\mathbb{C}}^n.$ Denote $H^p$($\Omega$) the Hardy space of $\Omega .$ Suppose that $S$ is $H^p$ interpolating with $p\ge 2.$ Then $S$ has the bounded linear extension property. The same is true for the Bergman spaces of the ball by use of the "Subordination Lemma". The point of view used here is the vectorial one: Hilbertian and Besselian basis.

The presentation is changed. The results and the proofs are the same

References in corpus (1)

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