Factorization of some Hardy-type spaces of holomorphic functions

Aline Bonami; Luong Dang Ky

doi:10.1016/j.crma.2014.09.004

Harmonic analysis

Factorization of some Hardy-type spaces of holomorphic functions

Presented by: Yves Meyer

Aline Bonami ¹; Luong Dang Ky 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, Volume 352 (2014) no. 10, pp. 817-821.

Abstract
Résumé

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.

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.

Received: 2014-06-20
Accepted: 2014-09-08
Published online: 2014-09-26

DOI: 10.1016/j.crma.2014.09.004

Author's affiliations:

Aline Bonami ¹; Luong Dang Ky 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

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     title = {Factorization of some {Hardy-type} spaces of holomorphic functions},
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Aline Bonami; Luong Dang Ky. Factorization of some Hardy-type spaces of holomorphic functions. Comptes Rendus. Mathématique, Volume 352 (2014) no. 10, pp. 817-821. doi : 10.1016/j.crma.2014.09.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.004/

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Cited by

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[9] L.D. Ky New Hardy spaces of Musielak–Orlicz type and boundedness of sublinear operators, Integral Equ. Oper. Theory, Volume 78 (2014) no. 1, pp. 115-150

[10] Y. Liang; J. Huang; D. Yang New real-variable characterizations of Musielak–Orlicz Hardy spaces, J. Math. Anal. Appl., Volume 395 (2012) no. 1, pp. 413-428

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