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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Truncations of multilinear Hankel operators


Authors: Aline Bonami, Sandrine Grellier and Mohammad Kacim
Journal: Trans. Amer. Math. Soc. 360 (2008), 1377-1390
MSC (2000): Primary 47B35; Secondary 42A50, 47A63, 47B10, 47B49
Published electronically: October 3, 2007
MathSciNet review: 2357699
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Abstract: We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are still bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.


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Additional Information

Aline Bonami
Affiliation: MAPMO, Université d’Orléans, Faculté des Sciences, Département de Mathéma- tiques, BP 6759, F 45067 Orleans Cédex 2, France
Email: bonami@labomath.univ-orleans.fr

Sandrine Grellier
Affiliation: MAPMO, Université d’Orléans, Faculté des Sciences, Département de Mathéma- tiques, BP 6759, F 45067 Orleans Cédex 2, France
Email: grellier@labomath.univ-orleans.fr

Mohammad Kacim
Affiliation: Université Saint-Joseph, Rue de Damas, Beirut 1104-2020, Lebanon
Email: kacim76@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04185-2
PII: S 0002-9947(07)04185-2
Keywords: Hankel operator, truncation, Hardy spaces, Lipschitz spaces, bilinear Hilbert transform
Received by editor(s): November 22, 2004
Received by editor(s) in revised form: October 7, 2005
Published electronically: October 3, 2007
Additional Notes: The authors were partially supported by the 2002-2006 IHP Network, Contract Number: HPRN-CT-2002-00273 - HARP
The authors would like to thank Joaquim Bruna who suggested this problem.
Article copyright: © Copyright 2007 American Mathematical Society