Comptes Rendus
no. 11
An inner function which is not weak outer
[Une fonction intérieure qui n'est pas faiblement extérieure]
Evgueni Doubtsov1
1Department of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnaya pl. 2, St. Petersburg 198904, Russia
Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 957-960

We construct a nonvanishing inner function I in the unit ball B⊂ℂ n such that the subspace IHp(B) is not weakly dense in the Hardy space Hp(B), with 0<p<1.

On construit une fonction intérieure I dans la boule unité B⊂ℂ n telle que I(z)≠0 pour z∈B et le sous-espace IHp(B) n'est pas faiblement dense dans la classe de Hardy Hp(B), pour 0<p<1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02374-9

Evgueni Doubtsov  1

1 Department of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnaya pl. 2, St. Petersburg 198904, Russia 
Evgueni Doubtsov. An inner function which is not weak outer. Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 957-960. doi: 10.1016/S1631-073X(02)02374-9
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[8] K. Zhu Operator Theory in Function Spaces, Marcel Dekker, New York, 1990

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