Factorization of some Hardy-type spaces of holomorphic functions

Bonami, Aline; Ky, Luong Dang

doi:10.1016/j.crma.2014.09.004

Harmonic analysis

Factorization of some Hardy-type spaces of holomorphic functions
[Factorisation de fonctions holomorphes dans des espaces de type Hardy]

Présenté par : Yves Meyer

Bonami, Aline ¹ ; Ky, Luong Dang ²

¹ MAPMO–UMR 6628, Département de mathématiques, Université d'Orléans, 45067 Orléans cedex 2, France
² Department of Mathematics, University of Quy Nhon, 170 An Duong Vuong, Quy Nhon, Binh Dinh, Vietnam

Comptes Rendus. Mathématique, Tome 352 (2014) no. 10, pp. 817-821.

Résumé
Abstract

Nous démontrons que le produit ponctuel de deux fonctions holomorphes du demi-plan supérieur, l'une dans l'espace de Hardy $H^{1}$ , l'autre dans son dual, appartiennent à un espace de type Hardy. À l'inverse, chaque fonction holomorphe de cet espace peut s'écrire sous la forme d'un tel produit. Ceci généralise un résultat connu dans le cas du disque unité.

We prove that the pointwise product of two holomorphic functions of the upper half-plane, one in the Hardy space $H^{1}$ , the other one in its dual, belongs to a Hardy-type space. Conversely, every holomorphic function in this space can be written as such a product. This generalizes a previous characterization in the context of the unit disc.

Reçu le : 2014-06-20
Accepté le : 2014-09-08
Publié le : 2014-09-26

DOI : 10.1016/j.crma.2014.09.004

Affiliations des auteurs :

Bonami, Aline ¹ ; Ky, Luong Dang ²

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     title = {Factorization of some {Hardy-type} spaces of holomorphic functions},
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Bonami, Aline; Ky, Luong Dang. Factorization of some Hardy-type spaces of holomorphic functions. Comptes Rendus. Mathématique, Tome 352 (2014) no. 10, pp. 817-821. doi : 10.1016/j.crma.2014.09.004. http://www.numdam.org/articles/10.1016/j.crma.2014.09.004/

Bibliographie
Cité par

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