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Hankel operators with unbounded symbols

Author(s): P. Ahern; E. H. Youssfi
Journal: Proc. Amer. Math. Soc. 135 (2007), 1865-1873.
MSC (2000): Primary 47B35, 32A35, 32A25
Posted: November 7, 2006
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Abstract: We prove that there are holomorphic functions $ f$ in the Hardy space of the unit ball or the bidisc such that the big Hankel operator with symbol $ \bar f$ is bounded and for any holomorphic function $ g$ the function $ \bar f + g$ cannot be bounded.

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Additional Information:

P. Ahern
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53705
Email: ahern@math.wisc.edu

E. H. Youssfi
Affiliation: LATP, U.M.R. C.N.R.S. 6632, CMI, Université de Provence, 39 Rue F-Joliot-Curie, 13453 Marseille Cedex 13, France
Email: youssfi@gyptis.univ-mrs.fr

DOI: 10.1090/S0002-9939-06-08675-8
PII: S 0002-9939(06)08675-8
Received by editor(s): November 24, 2005
Received by editor(s) in revised form: February 16, 2006
Posted: November 7, 2006
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2006, American Mathematical Society

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