Journal of the Australian Mathematical Society

Research Article

Wavelet decomposition of Calderón-Zygmund operators on function spaces

Ka-Sing Laua1 and Lixin Yana2

a1 Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong e-mail: kslau@math.cuhk.edu.hk

a2 Department of Mathematics, Zhongshan University, Guangzhou, 510275, P. R. China e-mail: lixin@ics.mq.edu.au

Abstract

We make use of the Beylkin-Coifman-Rokhlin wavelet decomposition algorithm on the Calderón-Zygmund kernel to obtain some fine estimates on the operator and prove the T(l) theorem on Besov and Triebel-Lizorkin spaces. This extends previous results of Frazier et al., and Han and Hofmann.

(Received December 18 2000)

(Revised March 01 2003)

2000 Mathematics subject classification

  • primary 42B20;
  • 46B30

Keywords and phrases

  • Calderón-Zygmund operator;
  • Besov space;
  • Triebel-Lizorkin space;
  • wavelet;
  • BCR algorithm