Wavelet characterization of weighted spaces
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We give a characterization of weighted Hardy spaces Hp(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.
Math Subject Classifications42B20 42B25 42B30 46B15
Key Words and Phraseswavelets Hp spaces Ap weights vector-valued Calderón-Zygmund operators Littlewood-Paley theory unconditional bases
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