Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (4): 1618-1632.doi: 10.1007/s10473-023-0411-1

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BOUNDEDNESS OF THE CALDERÓN COMMUTATOR WITH A ROUGH KERNEL ON TRIEBEL-LIZORKIN SPACES

Guoen HU, Jie LIU   

  1. Center of Fundamental Science, Huanghe Science and Technology University, Zhengzhou 450063, China
  • Received:2022-04-17 Revised:2022-06-27 Published:2023-08-08
  • Contact: †Guoen HU, E-mail: guoenxx@163.com
  • About author:Jie LIU, E-mail: 57923206@qq.com
  • Supported by:
    *The research was supported by the NNSF of China (11871108).

Abstract: In this paper, we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calderón commutator defined by TΩ,af(x)=p.v.RdΩ(xy)|xy|d+1(a(x)a(y))f(y)dy, where Ω is homogeneous of degree zero, integrable on Sd1 and has a vanishing moment of order one, and a is a function on Rd such that aL(Rd). We prove that if 1<p,q< and ΩL(logL)2q~(Sd1) with q~=max{1/q,1/q}, then TΩ,a is bounded on Triebel-Lizorkin spaces F˙p0,q(Rd).

Key words: Calderón commutator, Fourier transform, Littlewood-Paley theory, Calderón reproducing formula

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