数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1919-1928.doi: 10.1016/S0252-9602(12)60149-0

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Sp-CLASS (0 <p < ∞) TOEPLITZ OPERATOR WITH UNBOUNDED SYMBOL ON DIRICHLET SPACE

夏锦|王晓峰*|曹广福   

  1. College of Mathematics, Guangzhou University, Guangzhou 510006, China|Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Highter Education Institutes, Guangzhou University, Guangzhou 51006, China
  • 收稿日期:2011-02-21 出版日期:2012-09-20 发布日期:2012-09-20
  • 通讯作者: 王晓峰,wangxiaofeng514@tom.com E-mail:xiaj@cdut.edu.cn; wangxiaofeng514@tom.com; guangfucao@163.com
  • 基金资助:

    The research was partly supported by NSFC (10971040).

Sp-CLASS (0 <p < ∞) TOEPLITZ OPERATOR WITH UNBOUNDED SYMBOL ON DIRICHLET SPACE

 XIA Jin, WANG Xiao-Feng*, CAO Guang-Fu   

  1. College of Mathematics, Guangzhou University, Guangzhou 510006, China|Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Highter Education Institutes, Guangzhou University, Guangzhou 51006, China
  • Received:2011-02-21 Online:2012-09-20 Published:2012-09-20
  • Contact: WANG Xiao-Feng, wangxiaofeng514@tom.com E-mail:xiaj@cdut.edu.cn; wangxiaofeng514@tom.com; guangfucao@163.com
  • Supported by:

    The research was partly supported by NSFC (10971040).

摘要:

In this paper, we construct a function u in L2,1(Bn, dA), which is unbounded on any neighborhood of each boundary point of Bn, such that Toeplitz operator Tu is com-pact on Dirichlet space D(Bn, dA). Furthermore, Schatten p-class (0 < p < ∞) Toeplitz operators on Dirichlet space D(Bn, dA) with unbounded symbols are also obtained.

关键词: Toeplitz operator, Dirichlet space, Schatten p-class operator

Abstract:

In this paper, we construct a function u in L2,1(Bn, dA), which is unbounded on any neighborhood of each boundary point of Bn, such that Toeplitz operator Tu is com-pact on Dirichlet space D(Bn, dA). Furthermore, Schatten p-class (0 < p < ∞) Toeplitz operators on Dirichlet space D(Bn, dA) with unbounded symbols are also obtained.

Key words: Toeplitz operator, Dirichlet space, Schatten p-class operator

中图分类号: 

  • 35D10