On linear extension for interpolating sequences

Volume 186 / 2008

Eric Amar Studia Mathematica 186 (2008), 251-265 MSC: 42B30, 46J15, 32A35. DOI: 10.4064/sm186-3-4


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


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

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