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    YANG, Qixiang and DING, Yong 2016. Fast algorithm for calderón-zygmund operators: convergence speed and rough kernel. Acta Mathematica Scientia, Vol. 36, Issue. 2, p. 345.


    Yu, Yunxia and Yang, Zhanying 2013. An Approximation Method for Convolution Calderón-Zygmund Operators. Abstract and Applied Analysis, Vol. 2013, p. 1.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 77, Issue 1
  • August 2004, pp. 29-46

Wavelet decomposition of Calderón-Zygmund operators on function spaces

  • Ka-Sing Lau (a1) and Lixin Yan (a2)
  • DOI: http://dx.doi.org/10.1017/S1446788700010132
  • Published online: 01 April 2009
Abstract
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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]J. Aguirre , M. Escobedo , J. C. Perel and Ph. Tchamitchian , ‘Basis of wavelets and atomic decompositions of H1 (Rn) and H1 (Rn × Rn),’, Proc. Amer. Math. Soc. 111 (1991), 683693.

[2]G. Beylkin , R. Coifman and V. Rokhlin , ‘Fast wavelet transforms and numerical algorithms’, Comm. Pure Appl. Math. 44 (1991), 141183.

[3]I. Daubechies , Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Appl. Math. 61 (SIAM, Philadelphia, 1992).

[4]G. David and J. L. Journé , ‘A boundedness criterion for generalized Calderón-Zygmund operators’, Ann. of Math. 120 (1984), 371397.

[6]M. Frazier , B. Jawerth and G. Weiss , Littlewood-Paley theory and the study of functions, CBMS– Regional Conference Series in Mathematics 79 (AMS, Providence, RI, 1991).

[9]Y. Han , M. Paluszynski and G. Weiss , ‘A new atomic decomposition for the Triebel-Lizorkin spaces’, Contemporary Math. 189 (1995), 235249.

[10]P. G. Lemarié , ‘Continuité sur les espaces de Besov and operatéurs definis par des intégrales singulières’, Ann. Inst. Fourier (Grenoble)35 (1985), 175187.

[13]H. Triebel , Theory of function spaces (Birkhäuser, Basel, 1983).

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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