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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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. https://www.numdam.org/articles/10.1016/j.crma.2014.09.004/

Bibliographie
Cité par

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Bakas, Odysseas; Xu, Zhendong; Zhai, Yujia; Zhang, Hao Multiplication between elements in martingale Hardy spaces and their dual spaces, Journal of Functional Analysis, Volume 287 (2024) no. 2, p. 110467 | DOI:10.1016/j.jfa.2024.110467
Bonami, Aline; Jiao, Yong; Xie, Guangheng; Yang, Dachun; Zhou, Dejian Products and commutators of martingales in H1 and BMO, Journal de Mathématiques Pures et Appliquées, Volume 180 (2023), p. 188 | DOI:10.1016/j.matpur.2023.10.001
Bonami, Aline; Ky, Luong Dang; Liang, Yiyu; Yang, Dachun Several remarks on Musielak–Orlicz Hardy spaces, Bulletin des Sciences Mathématiques, Volume 181 (2022), p. 103206 | DOI:10.1016/j.bulsci.2022.103206
Zhang, Yangyang; Yang, Dachun; Yuan, Wen Real-variable characterizations of local Orlicz-slice Hardy spaces with application to bilinear decompositions, Communications in Contemporary Mathematics, Volume 24 (2022) no. 06 | DOI:10.1142/s0219199721500048
Yang, Dachun; Yuan, Wen; Zhang, Yangyang Bilinear decomposition and divergence-curl estimates on products related to local Hardy spaces and their dual spaces, Journal of Functional Analysis, Volume 280 (2021) no. 2, p. 108796 | DOI:10.1016/j.jfa.2020.108796
Bonami, Aline; Cao, Jun; Ky, Luong Dang; Liu, Liguang; Yang, Dachun; Yuan, Wen Multiplication between Hardy spaces and their dual spaces, Journal de Mathématiques Pures et Appliquées, Volume 131 (2019), p. 130 | DOI:10.1016/j.matpur.2019.05.003
Bonami, Aline; Feuto, Justin; Grellier, Sandrine; Ky, Luong Dang Atomic decomposition and weak factorization in generalized Hardy spaces of closed forms, Bulletin des Sciences Mathématiques, Volume 141 (2017) no. 7, p. 676 | DOI:10.1016/j.bulsci.2017.07.004
Yang, Dachun; Liang, Yiyu; Ky, Luong Dang Paraproducts and Products of Functions in B M O ( ℝ n ) $BMO (R^{n})$ and H 1 ( ℝ n ) $H^{1} (R^{n})$ Through Wavelets, Real-Variable Theory of Musielak-Orlicz Hardy Spaces, Volume 2182 (2017), p. 397 | DOI:10.1007/978-3-319-54361-1_10

Cité par 8 documents. Sources : Crossref