Comptes Rendus
no. 11
An inner function which is not weak outer
[Une fonction intérieure qui n'est pas faiblement extérieure]
Evgueni Doubtsov1
1 Department 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.

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.

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.

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 
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02374-9/

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[6] H.S. Shapiro Some remarks on weighted polynomial approximation of holomorphic functions, Mat. Sb., Volume 73(115) (1967) no. 3, pp. 320-330 (in Russian)

[7] J.H. Shapiro Remarks on F-spaces of analytic functions, Lecture Notes in Math., 604, Springer-Verlag, 1977, pp. 107-124

[8] K. Zhu Operator Theory in Function Spaces, Marcel Dekker, New York, 1990

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