On linear extension for interpolating sequences

• Autorzy: Eric Amar
• Języki publikacji: EN

Abstrakty

EN

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 $H^{∞}(𝔹)$ then S is $H^{p}(𝔹)$-interpolating with a linear extension operator for any 1 ≤ p < ∞. Already in this case this is a new result.

Kategorie tematyczne

• 32A35: H p -spaces, Nevanlinna spaces
• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 186
• Numer: 3
• Strony: 251-265

Daty

wydano

2008

Twórcy

autor

Eric Amar

• Université Bordeaux I, 351 Cours de la Libération, 33405 Talence, France

Identyfikatory

DOI

10.4064/sm186-3-4