On démontre que l'opérateur de Hankel associé au projecteur de Szegö sur la boule unité s'étend continûment à l'espace de Hardy si et seulement si b est à oscillation moyenne logarithmique sur la sphère unité.
We prove that the Hankel operator associated to the Szegö projection on the unit ball is bounded on the Hardy space if and only if its symbol b has logarithmic mean oscillation on the unit sphere.
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@article{CRMATH_2007__344_12_749_0, author = {Bonami, Aline and Grellier, Sandrine and Sehba, Beno{\^\i}t F.}, title = {Boundedness of {Hankel} operators on $ {\mathcal{H}}^{1}({\mathbb{B}}^{n})$}, journal = {Comptes Rendus. Math\'ematique}, pages = {749--752}, publisher = {Elsevier}, volume = {344}, number = {12}, year = {2007}, doi = {10.1016/j.crma.2007.05.004}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.05.004/} }
TY - JOUR AU - Bonami, Aline AU - Grellier, Sandrine AU - Sehba, Benoît F. TI - Boundedness of Hankel operators on $ {\mathcal{H}}^{1}({\mathbb{B}}^{n})$ JO - Comptes Rendus. Mathématique PY - 2007 SP - 749 EP - 752 VL - 344 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.05.004/ DO - 10.1016/j.crma.2007.05.004 LA - en ID - CRMATH_2007__344_12_749_0 ER -
%0 Journal Article %A Bonami, Aline %A Grellier, Sandrine %A Sehba, Benoît F. %T Boundedness of Hankel operators on $ {\mathcal{H}}^{1}({\mathbb{B}}^{n})$ %J Comptes Rendus. Mathématique %D 2007 %P 749-752 %V 344 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.05.004/ %R 10.1016/j.crma.2007.05.004 %G en %F CRMATH_2007__344_12_749_0
Bonami, Aline; Grellier, Sandrine; Sehba, Benoît F. Boundedness of Hankel operators on $ {\mathcal{H}}^{1}({\mathbb{B}}^{n})$. Comptes Rendus. Mathématique, Tome 344 (2007) no. 12, pp. 749-752. doi : 10.1016/j.crma.2007.05.004. http://archive.numdam.org/articles/10.1016/j.crma.2007.05.004/
[1] A. Bonami, S. Grellier, Decomposition theorems for Hardy–Orlicz spaces and weak factorization, Preprint, 2007
[2] Factorization of Hardy spaces and Hankel operators on convex domains in , J. Geom. Anal., Volume 11 (2001) no. 3, pp. 363-397
[3] On the action of Hankel and Toeplitz operators on some function spaces, Duke Math. J., Volume 51 (1984) no. 4, pp. 937-958
[4] Function Theory in the Unit Ball of , 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] and Carleson measures, Trans. Amer. Math. Soc., Volume 287 (1985) no. 1, pp. 107-126
[6] Hankel and Toeplitz operators in Hardy spaces, Soviet Math., Volume 37 (1987), pp. 1359-1364
[7] On logarithmic Carleson measures, Acta Sci. Math. (Szeged), Volume 69 (2003), pp. 605-618
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