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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 46, Pages 2929-2945
http://dx.doi.org/10.1155/S0161171203212035

Toeplitz operators with BMO symbols and the Berezin transform

Department of Mathematics, University of Manitoba, Winnipeg, Manitobia R3T 2N2, Canada

Received 3 December 2002

Copyright © 2003 Hindawi Publishing Corporation. 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 prove that the boundedness and compactness of the Toeplitz operator on the Bergman space with a BMO1 symbol is completely determined by the boundary behaviour of its Berezin transform. This result extends the known results in the cases when the symbol is either a positive L1-function or an L function.