On linear extension for interpolating sequences

Eric Amar

Studia Mathematica, Tome 187 (2008), p. 251-265 / Harvested from The Polish Digital Mathematics Library

Résumé

Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces $H^{p}(σ)$ and the $H^{p}(σ)$ interpolating sequences S in the p-spectrum $ℳ _{p}$ of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is $H^{s}(σ)$-interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in $H^{∞}()$ then S is $H^{p}()$-interpolating with a linear extension operator for any 1 ≤ p < ∞. Already in this case this is a new result.

Détail

Publié le : 2008-01-01

Zbl 1206.42022

EUDML-ID : urn:eudml:doc:284868