Wavelet Characterization of Weighted Spaces

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(infinity). We improve the previously known results and adopt a systematic point of view based upon the theory of vector-valued Calderon-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.