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Hankel operators with unbounded symbols

Authors: P. Ahern and E. H. Youssfi
Journal: Proc. Amer. Math. Soc. 135 (2007), 1865-1873
MSC (2000): Primary 47B35, 32A35, 32A25
Published electronically: November 7, 2006
MathSciNet review: 2286098
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Abstract | References | Similar Articles | Additional Information

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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  • [BT] Mihály Bakonyi and Dan Timotin, On a conjecture of Cotlar and Sadosky on multidimensional Hankel operators, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 10, 1071–1075 (English, with English and French summaries). MR 1614007, 10.1016/S0764-4442(97)88707-1
  • [C] L. A. Coburn, Toeplitz operators, quantum mechanics, and mean oscillation in the Bergman metric, Operator theory: operator algebras and applications, Part 1 (Durham, NH, 1988) Proc. Sympos. Pure Math., vol. 51, Amer. Math. Soc., Providence, RI, 1990, pp. 97–104. MR 1077380
  • [CS] Mischa Cotlar and Cora Sadosky, Two distinguished subspaces of product BMO and Nehari-AAK theory for Hankel operators on the torus, Integral Equations Operator Theory 26 (1996), no. 3, 273–304. MR 1415032, 10.1007/BF01306544
  • [FS] Sarah H. Ferguson and Cora Sadosky, Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures, J. Anal. Math. 81 (2000), 239–267. MR 1785283, 10.1007/BF02788991
  • [J] Stefan Jakobsson, The harmonic Bergman kernel and the Friedrichs operator, Ark. Mat. 40 (2002), no. 1, 89–104. MR 1948888, 10.1007/BF02384504
  • [S] E. Strouse, Conference in Holomorphic Function Spaces and their Operators, CIRM Marseille, 2002.
  • [Z1] Ke He Zhu, Operator theory in function spaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 139, Marcel Dekker, Inc., New York, 1990. MR 1074007
  • [Z2] Kehe Zhu, Spaces of holomorphic functions in the unit ball, Graduate Texts in Mathematics, vol. 226, Springer-Verlag, New York, 2005. MR 2115155

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Additional Information

P. Ahern
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53705

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

Received by editor(s): November 24, 2005
Received by editor(s) in revised form: February 16, 2006
Published electronically: November 7, 2006
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society