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How Fast and in what Sense(s) Does the Calderón Reproducing Formula Converge?

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Abstract

We prove that a very general form of the Calderón reproducing formula converges in L p(w), for all 1<p<∞, whenever w belongs to the Muckenhoupt class A p . We show that the formula converges whether we interpret its defining integral, in very natural senses, as a limit of L p(w)-valued Riemann or Lebesgue integrals. We give quantitative estimates on their rates of convergence (or, equivalently, on the speed at which the errors go to 0) in L p(w).

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  1. University of Vermont, Burlington, VT, 05405, USA

    M. Wilson

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  1. M. Wilson
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Correspondence to M. Wilson.

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Communicated by Fernando Soria.

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Wilson, M. How Fast and in what Sense(s) Does the Calderón Reproducing Formula Converge?. J Fourier Anal Appl 16, 768–785 (2010). https://doi.org/10.1007/s00041-009-9109-6

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  • DOI: https://doi.org/10.1007/s00041-009-9109-6

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