Hankel operators with unbounded symbols
HTML articles powered by AMS MathViewer
- by P. Ahern and E. H. Youssfi PDF
- Proc. Amer. Math. Soc. 135 (2007), 1865-1873 Request permission
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.References
- 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, DOI 10.1016/S0764-4442(97)88707-1
- 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, DOI 10.2140/paa.2019.1.327
- 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, DOI 10.1007/BF01306544
- 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, DOI 10.1007/BF02788991
- Stefan Jakobsson, The harmonic Bergman kernel and the Friedrichs operator, Ark. Mat. 40 (2002), no. 1, 89–104. MR 1948888, DOI 10.1007/BF02384504
- E. Strouse, Conference in Holomorphic Function Spaces and their Operators, CIRM Marseille, 2002.
- 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
- Kehe Zhu, Spaces of holomorphic functions in the unit ball, Graduate Texts in Mathematics, vol. 226, Springer-Verlag, New York, 2005. MR 2115155
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
- 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
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 1865-1873
- MSC (2000): Primary 47B35, 32A35, 32A25
- DOI: https://doi.org/10.1090/S0002-9939-06-08675-8
- MathSciNet review: 2286098