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Algebra of Calderón-Zygmund Operators Associated to Para-Accretive Functions

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Abstract

By use of special wavelet bases associated to accretive or pseudo-accretive functions, it was proved that all Calderón-Zygmund operators satisfying certain conditions form an algebra. In this article, a similar result is proved for more general para-accretive functions. Since wavelet bases are not available for this general setting, the new idea used here is to apply the discrete Calderón-type reproducing formula associated to para-accretive functions developed in [14]. This new method can be applied to many other problems, where wavelet bases are not available.

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Authors and Affiliations

  1. Department of Mathematics, Auburn University, Auburn, Alabama 36849-5310, USA

    Yongsheng Han

  2. Institute of Mathematics, Academia Sinica, Taipei, Taiwan 115, Republic of China

    Ming-Yi Lee

  3. Department of Mathematics, National Central University, Chung-Li, Taiwan 320, Republic of China

    Chin-Cheng Lin

Authors
  1. Yongsheng Han
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  2. Ming-Yi Lee
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  3. Chin-Cheng Lin
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Correspondence to Yongsheng Han, Ming-Yi Lee or Chin-Cheng Lin.

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Han, Y., Lee, MY. & Lin, CC. Algebra of Calderón-Zygmund Operators Associated to Para-Accretive Functions. J Fourier Anal Appl 12, 581–596 (2006). https://doi.org/10.1007/s00041-006-6035-8

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  • DOI: https://doi.org/10.1007/s00041-006-6035-8

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