TOEPLITZ OPERATORS WITH BMO SYMBOLS ON THE SEGAL-BARGMANN SPACE

We show that Zorboska's criterion for compactness of Toeplitz operators with BMO1 symbols on the Bergman space of the unit disc holds, by a different proof, for the Segal-Bargmann space of Gaussian square-integrable entire functions on C-n. We establish some basic properties of BMOp for p >= 1 and complete the characterization of bounded and compact Toeplitz operators with BMO1 symbols. Via the Bargmann isometry and results of Lo and Englis, we also give a compactness criterion for the Gabor-Daubechies windowed Fourier localization operators on L-2(R-n, dv) when the symbol is in a BMO1 Sobolev-type space. Finally, we discuss examples of the compactness criterion and counterexamples to the unrestricted application of this criterion for the compactness of Toeplitz operators.