Compactness for the commutators of singular integral operators with rough variable kernels

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

Chen, Jiecheng¹  Chen, Yanping²  Hu, Guoen³ 

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

[2] Univ Sci & Technol Beijing, Dept Appl Math, Beijing 100083, Peoples R China

[3] Zhengzhou Informat Sci & Technol Inst, Dept Appl Math, Zhengzhou 450001, Peoples R China

关键词: Commutator;    Singular integral operator with variable kernel;    Maximal operator;    Compact operator;   

DOI  :  10.1016/j.jmaa.2015.05.081

来源: Elsevier

【 摘 要 】

Let T-Omega be the singular integral operator with variable kernel defined by T(Omega)f(x) = p. v. integral(n)(R) Omega(x, x -y)/broken vertical bar x - y)(n) f(y)dy, where Omega(x, y) is homogeneous of degree zero in the second variable y, and integral(Sn-1) Omega (x, z')d sigma(z') = 0 for any x is an element of R-n. In this paper, the authors prove that if Omega is an element of L-infinity(R-n) X L-q(Sn-1) for some q > 2(n - 1)/n, then the commutator generated by a CMO(R-n) function and T-Omega, and the associated lacunary maximal operator, are compact. on L-2(R-n). The associated continuous maximal commutator is also considered. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free