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Keywords:

  • Calderón-Zygmund operators;
  • function spaces;
  • wavelet frames MSC (2010) 42B20;
  • 42C40

Abstract

We present an extrapolation theorem for the convergence of sequences of Calderón-Zygmund operators on various function spaces. We show that if a sequence of Calderón-Zygmund operators with the same smoothness and decay parameters is convergent in operator norm on equation image, then it is also convergent as operators on equation image, 1 < p < ∞, and on a large class of Triebel-Lizorkin, Besov and Hardy spaces. As an application, we show that as the sampling density tends to the infinity, the wavelet frame operator tends to the identity in operator norm on Triebel-Lizorkin, Besov and Hardy spaces.