Toeplitz and Hankel Products on Bergman Spaces of the Unit Ball

被引：0
作者：
Yufeng LU Chaomei LIU School of Mathematical Sciences
机构：
来源：
Chinese Annals of Mathematics | 2009年 / 30卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Weighted Bergman space; Unit ball; Toeplitz operator; Hankel operator; Berezin transform;
D O I：
暂无
中图分类号：
O177 [泛函分析];
学科分类号：
070104 ;
摘要：
The authors give some new necessary conditions for the boundedness of Toeplitz products T_f~α T_■~α on the weighted Bergman space A_α~2 of the unit ball,where f and g are analytic on the unit ball.Hankel products H_fH_g~* on the weighted Bergman space of the unit ball are studied,and the results analogous to those Stroethoff and Zheng obtained in the setting of unit disk are proved.
引用
收藏
页码：293 / 310
页数：18
相关论文
共 18 条
[1]  
The distribution function inequality and products of Toeplitz operators and Hankel operators. Zheng D. Journal of Functional Analysis . 1996
[2]  
Spaces of Holomorphic Functions in the Unit Ball. Zhu,K. H. Graduate Texts in Mathematics . 2005
[3]  
Products of toeplitz operators on the bergman spaceAα2. Sandra Pott,Elizabeth Strouse. HPRI NCT . 2000
[4]  
Bounded Toeplitz products on the Bergman space of the unit ball in C~n. Park J D. Integral Equations and Operator Theory . 2006
[5]  
Bounded Toeplitz products on Bergman space of the unit ball. Stroethoff K,Zheng D C. J, Math. Anal. Appl . 2007
[6]  
Bounded Toeplitz products on the Bergman space of the polydisk. Stroethoff K,Zheng D. Journal of Mathematical Analysis and Applications . 2003
[7]   THE INVERTIBILITY OF THE PRODUCT OF UNBOUNDED TOEPLITZ-OPERATORS [J].
CRUZURIBE, D .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1994, 20 (02) :231-237
[8]   The distribution function inequality and products of Toeplitz operators and Hankel operators [J].
Zheng, DC .
JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 138 (02) :477-501
[9]  
Bounded Toeplitz Products on the Bergman Space of the Unit Ball in\mathbb{C}^n[J] . Jong-Do Park. &nbspIntegral Equations and Operator Theory . 2006 (4)
[10]  
Products of Hankel and Toeplitz operators on the Bergman space. Stroethoff,K.,Zheng,D. C. Journal of Functional Analysis . 1999
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