International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 46, Pages 2929-2945
Toeplitz operators with BMO symbols and the Berezin transform
Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Manitobia, Canada
Received 3 December 2002
Copyright © 2003 Nina Zorboska. 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.
We prove that the boundedness and compactness of the Toeplitz
operator on the Bergman space with a 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 -function or an function.