Journal of Operator Theory

Volume 61, Issue 2, Spring 2009 pp. 301-312.

Compactness of Hankel Operators on Hardy--Sobolev Spaces of the Polydisk

Authors: Patrick Ahern (1), El Hassan Youssfi (2), and Kehe Zhu (3)
Author institution: (1) Department of Mathematics, University of Wisconsin, Madison, WI 53705, USA
(2) LATP, U.M.R. C.N.R.S. 6632, CMI, Universite de Provence, 39 Rue F-Joliot-Curie, 13453 Marseille Cedex 13, France (3) Department of Mathematics, State University of New York, Albany, NY 12222, USA

Summary: We show that a big Hankel operator defined on certain Hardy--Sobolev spaces of the polydisk $\dn$, $n>1$, cannot be compact unless it is the zero operator. This result was obtained by Cotlar and Sadosky in 1993 for the classical Hardy space, but our approach here is much different and our result is more general.

Contents Full-Text PDF