International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 164843, 26 pages
http://dx.doi.org/10.1155/2011/164843
Research Article

Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

Roberto C. Raimondo1,2

1Division of Mathematics, Faculty of Statistics, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milan, Italy
2Department of Economics, University of Melbourne, Parkville, VIC 3010, Australia

Received 25 February 2011; Revised 5 June 2011; Accepted 6 June 2011

Academic Editor: B. N. Mandal

Copyright © 2011 Roberto C. Raimondo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the problem of the boundedness and compactness of 𝑇 𝜙 when 𝜙 ∈ 𝐿 2 ( Ω ) and Ω is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of 𝑇 𝜙 .