TOEPLITZ OPERATORS WITH BMO SYMBOLS ON THE SEGAL-BARGMANN SPACE

被引：39

作者：

Coburn, L. A. ^{[1
]}

Isralowitz, J. ^{[1
]}

Li, Bo ^{[1
]}

机构：

[1] SUNY Buffalo, Dept Math, Buffalo, NY 14260 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 363卷 / 06期

关键词：

COMPACT-OPERATORS; TRANSFORM;

D O I：

10.1090/S0002-9947-2011-05278-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：3015 / 3030

页数：16

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