The distribution function inequality and products of Toeplitz operators and Hankel operators

被引:70
作者
Zheng, DC
机构
[1] Department of Mathematics, Michigan State University, East Lansing
基金
美国国家科学基金会;
关键词
D O I
10.1006/jfan.1996.0073
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we study Hankel operators and Toeplitz operators through a distribution function inequality on the Lusin area integral function and the Littlewood-Paley theory. A sufficient condition and a necessary condition are obtained for the boundedness of the product of two Hankel operators. They lead to a way to approach Sarason's conjecture on products of Toeplitz operators and shed light on the compactness of the product of Hankel operators. An elementary necessary and sufficient condition for the product of two Toeplitz operators to be a compact perturbation of a Toeplitz operator is obtained. Moreover, a necessary condition is given for the product of Hankel operators to be in the commutator ideal of the algebra generated by the Toeplitz operators with symbols in a Sarason algebra. (C) 1996 Academic Press, Inc.
引用
收藏
页码:477 / 501
页数:25
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