Acta mathematica scientia,Series B ›› 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

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).

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

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