PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Interpolating sequences and Carleson measures in the Hardy–Sobolev spaces of the ball in ${\mathbb {C}}^{n}$

Volume 241 / 2018

E. Amar Studia Mathematica 241 (2018), 101-133 MSC: 32A35, 42B30. DOI: 10.4064/sm8405-8-2017 Published online: 30 October 2017

Abstract

We study interpolating sequences and Carleson measures for the Hardy–Sobolev spaces $ H_{s}^{p}$ in the ball ${\mathbb {B}}$ of $ {\mathbb {C}}^{n}$. Our main results for interpolating sequences $ S\subset {\mathbb {B}}$ of the multiplier algebra ${\mathcal {M}}_{s}^{p}$ of $ H_{s}^{p}$ are: (i) there is always a bounded linear extension operator $E: l^{\infty }\rightarrow {\mathcal {M}}_{s}^{p}$ realizing the interpolation; (ii) the union of two interpolating sequences $ S_{1}, S_{2}$ for ${\mathcal {M}}_{s}^{p}$ is interpolating for ${\mathcal {M}}_{s}^{p}$ if and only if $ S_{1}$ and $ S_{2}$ are completely separated, generalizing a theorem of Varopoulos. We also establish a link between dual boundedness and Carleson sequences with the interpolation property for the Hardy–Sobolev spaces $ H_{s}^{p}$.

Authors

  • E. AmarInstitut de Mathématiques de Bordeaux
    Université de Bordeaux
    F-33405 Talence, France
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image