O ct 2 00 6 ON LINEAR EXTENSION FOR INTERPOLATING SEQUENCES
نویسنده
چکیده
Let A be a uniform algebra on the compact space X and σ a probability measure on X . We define the Hardy spaces H(σ) and the H(σ) interpolating sequences S in the p-spectrum Mp of σ. We prove, under some structural hypotheses on σ that ”Carleson type” conditions on S imply that S is interpolating with a linear extension operator in H(σ), s < p provided that either p = ∞ or p ≤ 2. This gives new results on interpolating sequences for Hardy spaces of the ball and the polydisc. In particular in the case of the unit ball of C we get that if there is a sequence {ρa}a∈S bounded in H(B) such that ∀a, b ∈ S, ρa(b) = δab, then S is H (B)-interpolating with a linear extension operator for any 1 ≤ p < ∞.
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