A wavelet characterization for weighted Hardy Spaces

  • Sijue Wu

    New York University, USA


In this paper, we give a wavelet area integral characterization for weighted Hardy spaces Hp(ω),0<p<H^p(\omega), 0 < p < \infty, with ωA\omega \in A_\infty. Our wavelet characterization establishes the identification betweenHp(ω)H^p(\omega) and T2p(ω)T^p_2(\omega), the weighted discrete tent space, for 0<p<0 < p < \infty and ωA\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 Hp(ω)H^p(\omega) and the dual space of Hp(ω)H^{p'}(\omega) where 1<p<1 < p < \infty and 1/p+1/p=11/p + 1/p' = 1, and the wavelet and the Carleson measure characterizations of BMOω_\omega. Moreover, we obtain interpolation between AA_\infty-weighted Hardy spaces Hp1(ω)H^{p_1}(\omega) and Hp2(ω),1p1<p2<H^{p_2}(\omega), 1 ≤ p_1 < p_2 < \infty.

Cite this article

Sijue Wu, A wavelet characterization for weighted Hardy Spaces. Rev. Mat. Iberoam. 8 (1992), no. 3, pp. 329–349

DOI 10.4171/RMI/127