Abstract
We give a characterization of weighted Hardy spaces H p (w), valid for a rather large collection of wavelets, 0 <p ≤ 1,and weights w in the Muckenhoupt class A ∞ We improve the previously known results and adopt a systematic point of view based upon the theory of vector-valued Calderón-Zygmund operators. Some consequences of this characterization are also given, like the criterion for a wavelet to give an unconditional basis and a criterion for membership into the space from the size of the wavelet coefficients.
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García-Cuerva, J., Martell, J.M. Wavelet characterization of weighted spaces. J Geom Anal 11, 241–264 (2001). https://doi.org/10.1007/BF02921965
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DOI: https://doi.org/10.1007/BF02921965