Boundedness of Hankel operators on $ {\mathcal{H}}^{1}({\mathbb{B}}^{n})$

Aline Bonami; Sandrine Grellier; Benoît F. Sehba

doi:10.1016/j.crma.2007.05.004

Complex Analysis

Boundedness of Hankel operators on

H^{1} (B^{n})

Presented by: Yves Meyer

Aline Bonami ¹; Sandrine Grellier ¹; Benoît F. Sehba ²

¹ Fédération Denis-Poisson, MAPMO-UMR 6628, département de mathématiques, université d'Orléans, 45067 Orléans cedex 2, France
² Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK

Comptes Rendus. Mathématique, Volume 344 (2007) no. 12, pp. 749-752

Abstract (Original language)
Résumé

We prove that the Hankel operator $h_{b}$ associated to the Szegö projection on the unit ball $B^{n}$ is bounded on the Hardy space $H^{1} (B^{n})$ if and only if its symbol b has logarithmic mean oscillation on the unit sphere.

On démontre que l'opérateur de Hankel $h_{b}$ associé au projecteur de Szegö sur la boule unité s'étend continûment à l'espace de Hardy $H^{1} (B^{n})$ si et seulement si b est à oscillation moyenne logarithmique sur la sphère unité.

Received: 2007-02-09
Accepted: 2007-05-15
Published online: 2007-06-15

DOI: 10.1016/j.crma.2007.05.004

Author's affiliations:

Aline Bonami ¹; Sandrine Grellier ¹; Benoît F. Sehba ²

¹ Fédération Denis-Poisson, MAPMO-UMR 6628, département de mathématiques, université d'Orléans, 45067 Orléans cedex 2, France
² Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK

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     title = {Boundedness of {Hankel} operators on $ {\mathcal{H}}^{1}({\mathbb{B}}^{n})$},
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Aline Bonami; Sandrine Grellier; Benoît F. Sehba. Boundedness of Hankel operators on $ {\mathcal{H}}^{1}({\mathbb{B}}^{n})$. Comptes Rendus. Mathématique, Volume 344 (2007) no. 12, pp. 749-752. doi: 10.1016/j.crma.2007.05.004

References
Cited by

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[4] W. Rudin Function Theory in the Unit Ball of $C^{n}$ , Grundlehren der Mathematischen Wissenschaften, Fundamental Principles of Mathematical Science, vol. 241, Springer-Verlag, New York–Berlin, 1980 (xiii+436 pp) (ISBN: 0-387-90514-6)

[5] W.S. Smith $BMO (ρ)$ and Carleson measures, Trans. Amer. Math. Soc., Volume 287 (1985) no. 1, pp. 107-126

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[7] R. Zhao On logarithmic Carleson measures, Acta Sci. Math. (Szeged), Volume 69 (2003), pp. 605-618

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