Spectral theory of Toeplitz and Hankel operators on the Bergman space A1
Taskinen, J. and Virtanen, J. A. (2008) Spectral theory of Toeplitz and Hankel operators on the Bergman space A1. New York Journal of Mathematics, 14. pp. 305-323. ISSN 1076-9803
Official URL: http://nyjm.albany.edu/j/2008/14-15.html
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.