Harmonic analysis
Factorization of some Hardy-type spaces of holomorphic functions

Presented by: Yves Meyer

Bonami, Aline1; Ky, Luong Dang2
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.

We prove that the pointwise product of two holomorphic functions of the upper half-plane, one in the Hardy space H1, 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 H1, 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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.09.004
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 
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Bonami, Aline; Ky, Luong Dang. 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://www.numdam.org/articles/10.1016/j.crma.2014.09.004/

[1] Bonami, A.; Grellier, S. Hankel operators and weak factorization for Hardy–Orlicz spaces, Colloq. Math., Volume 118 (2010) no. 1, pp. 107-132

[2] Bonami, A.; Grellier, S.; Ky, L.D. Paraproducts and products of functions in BMO(Rn) and H1(Rn) through wavelets, J. Math. Pures Appl. (9), Volume 97 (2012) no. 3, pp. 230-241

[3] A. Bonami, S. Grellier, L.D. Ky, Hardy spaces of Musielak–Orlicz type on the half-plane, preprint.

[4] Bonami, A.; Iwaniec, T.; Jones, P.; Zinsmeister, M. On the product of functions in BMO and H1, Ann. Inst. Fourier (Grenoble), Volume 57 (2007) no. 5, pp. 1405-1439

[5] Cao, J.; Chang, D.-C.; Yang, D.; Yang, S. Riesz transform characterizations of Musielak–Orlicz–Hardy spaces Trans. Amer. Math. Soc. (to appear) or | arXiv

[6] Coifman, R.R.; Rochberg, R. Another characterization of BMO, Proc. Amer. Math. Soc., Volume 79 (1980) no. 2, pp. 249-254

[7] Garnett, J.B. Bounded Analytic Functions, Academic Press, New York, 1981

[8] Ky, L.D. Bilinear decompositions and commutators of singular integral operators, Trans. Amer. Math. Soc., Volume 365 (2013) no. 6, pp. 2931-2958

[9] Ky, L.D. 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] Liang, Y.; Huang, J.; Yang, D. 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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