On linear extension for interpolating sequences

Eric Amar

Studia Mathematica (2008)

  • Volume: 186, Issue: 3, page 251-265
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Eric Amar. "On linear extension for interpolating sequences." Studia Mathematica 186.3 (2008): 251-265. <http://eudml.org/doc/284868>.

@article{EricAmar2008,
abstract = {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.},
author = {Eric Amar},
journal = {Studia Mathematica},
keywords = {interpolating sequences; Carleson measure; Hardy spaces},
language = {eng},
number = {3},
pages = {251-265},
title = {On linear extension for interpolating sequences},
url = {http://eudml.org/doc/284868},
volume = {186},
year = {2008},
}

TY - JOUR
AU - Eric Amar
TI - On linear extension for interpolating sequences
JO - Studia Mathematica
PY - 2008
VL - 186
IS - 3
SP - 251
EP - 265
AB - 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.
LA - eng
KW - interpolating sequences; Carleson measure; Hardy spaces
UR - http://eudml.org/doc/284868
ER -

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