New York Journal of Mathematics
Volume 14 (2008) 305-323


Jari Taskinen and Jani A. Virtanen

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

Published: August 20, 2008
Keywords: Toeplitz operators, Hankel operators, compactness, Fredholmness, Bergman space
Subject: 47B35, 47A53, 32A36, 32A37

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1<p<∞; in particular bounded Toeplitz operators on A1 were characterized completely very recently but only for bounded symbols. We also consider compactness of Hankel operators on A1.


The first author was partially supported by the Väisälä foundation of the Finnish Academy of Science and Letters. The second author was supported by Academy of Finland Project 207048.

Author information

Department of Mathematics, University of Helsinki, 00014 Helsinki, Finland