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On separated Carleson sequences in the unit disc

Eric Amar

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The interpolating sequences $S$ for $H^{\infty }(\mathbb{D})$, the bounded holomorphic functions in the unit disc $\mathbb{D}$ of the complex plane $\mathbb{C}$, were characterized by L. Carleson using metric conditions on $S$. Alternatively, to characterize interpolating sequences we can use the existence in $H^{\infty }(\mathbb{D})$ of an infinity of functions $\lbrace \rho _{a}\rbrace _{a\in S}$, uniformly bounded in $\mathbb{D}$, the function $\rho _{a}$ being $1$ at the point $a\in S$ and $0$ at any $b\in S\setminus \lbrace a\rbrace$. A. Hartmann recently proved that just one function in $H^{\infty }(\mathbb{D})$ was enough to characterize interpolating sequences for $H^{\infty }(\mathbb{D})$. In this work we use the "hard" part of Carleson's proof of the corona theorem to extend Hartmann's result and to answer a question he asked in his paper.

Article information

Publ. Mat., Volume 58, Number 2 (2014), 401-414.

First available in Project Euclid: 21 July 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30H10: Hardy spaces 30H80: Corona theorems

Interpolating sequences Carleson measures


Amar, Eric. On separated Carleson sequences in the unit disc. Publ. Mat. 58 (2014), no. 2, 401--414.

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