A wavelet characterization for weighted Hardy Spaces

Abstract

In this paper, we give a wavelet area integral characterization for weighted Hardy spaces H^p(\omega), 0 < p < \infty , with \omega \in A_\infty . Our wavelet characterization establishes the identification between H^p(\omega) and T^p_2(\omega) , the weighted discrete tent space, for 0 < p < \infty and \omega \in A_\infty . This allows us to use all the results of tent spaces for weighted Hardy spaces. In particular, we obtain the isomorphism between H^p(\omega) and the dual space of H^{p'}(\omega) where 1 < p < \infty and 1/p + 1/p' = 1 , and the wavelet and the Carleson measure characterizations of BMO _\omega . Moreover, we obtain interpolation between A_\infty -weighted Hardy spaces H^{p_1}(\omega) and H^{p_2}(\omega), 1 ≤ p_1 < p_2 < \infty .