数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (5): 1373-1384.doi: 10.1016/S0252-9602(17)30079-6

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COMPACTNESS FOR THE COMMUTATOR OF BOCHNER-RIESZ OPERATOR

卜瑞1, 陈杰诚2, 胡国恩3   

  1. 1. Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China;
    2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;
    3. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China
  • 收稿日期:2016-02-21 修回日期:2016-10-30 出版日期:2017-10-25 发布日期:2017-10-25
  • 通讯作者: Guoen HU,E-mail:guoenxx@163.com E-mail:guoenxx@163.com
  • 作者简介:Rui BU,E-mail:burui0@163.com;Jiecheng CHEN,E-mail:jcchen@zjnu.edu.cn
  • 基金资助:

    The research of Bu was supported by the NNSF of China (11571306), and the research of Chen was supported by the NNSF of China (11271330 and 11671363), and the research of Hu was supported by the NNSF of China (11371370).

COMPACTNESS FOR THE COMMUTATOR OF BOCHNER-RIESZ OPERATOR

Rui BU1, Jiecheng CHEN2, Guoen HU3   

  1. 1. Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China;
    2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;
    3. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China
  • Received:2016-02-21 Revised:2016-10-30 Online:2017-10-25 Published:2017-10-25
  • Contact: Guoen HU,E-mail:guoenxx@163.com E-mail:guoenxx@163.com
  • Supported by:

    The research of Bu was supported by the NNSF of China (11571306), and the research of Chen was supported by the NNSF of China (11271330 and 11671363), and the research of Hu was supported by the NNSF of China (11371370).

摘要:

Let α ∈ (0,(n-1)/2) and Tα be the Bochner-Riesz operator of order α.In this paper,for n=2 and n ≥ 3,the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO (Rn) function and Tα.

关键词: Bochner-Riesz operator, commutator, compact operator, Fourier transform estimate

Abstract:

Let α ∈ (0,(n-1)/2) and Tα be the Bochner-Riesz operator of order α.In this paper,for n=2 and n ≥ 3,the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO (Rn) function and Tα.

Key words: Bochner-Riesz operator, commutator, compact operator, Fourier transform estimate