数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 217-227.

• 论文 •    下一篇

单位球上Dirichlet型空间到Zμ型空间的积分型算子

赵艳辉1, 张学军2   

  1. 1 湖南科技学院理学院 湖南永州 425199;
    2 湖南师范大学数学与计算机科学学院 长沙 410006
  • 收稿日期:2016-07-11 修回日期:2016-12-17 出版日期:2017-04-26 发布日期:2017-04-26
  • 通讯作者: 赵艳辉 E-mail:1261450046@qq.com
  • 基金资助:
    国家自然科学基金(11571104)和湖南省自然科学基金(2015JJ2095)

On an Integral-Type Operator from Dirichlet Spaces to Zygmund Type Spaces on the Unit Ball

Zhao Yanhui1, Zhang Xuejun2   

  1. 1 College of Science, Hunan University of Science and Engineering, Hunan Yongzhou 425199;
    2 College of Mathematics and Computer Science, Hunan Normal University, Changsha 410006
  • Received:2016-07-11 Revised:2016-12-17 Online:2017-04-26 Published:2017-04-26
  • Supported by:
    Supported by the NSFC (11571104) and the Natural Science Foundation of Hunan Province (2015JJ2095)

摘要: 该文利用泛函分析以及多复变的方法,研究了单位球B上Dirichlet型空间Dp到Zygmund型空间Zμ的积分型算子的有界性和紧性问题.获得了单位球上Dirichlet型空间到Zygmund型空间的积分型算子为有界算子和紧算子的充要条件.

关键词: Dirichlet型空间, Zygmund型空间, 积分型算子, 有界性, 紧性

Abstract: Some questions of integral-type Operator from Dirichlet space to Zygmund type spaces in the unit ball were studied in this paper. By the methods of functional analysis and several complex variables, the necessary and sufficient conditions are given for integral-type operator to be bounded and compact from Dirichlet space to Zygmund type spaces in the unit ball.

Key words: Dirichlet space, Zygmund type spaces, Integral-type operator, Bounded, Compact

中图分类号: 

  • O174.56