On linear extension for interpolating sequences
Eric Amar2008, Studia Mathematica
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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 pspectrum Mp 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 C n 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 < ∞.
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