Revista Matemática Iberoamericana

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Volume 8, Issue 3, 1992, pp. 329–349
DOI: 10.4171/RMI/127

Published online: 1992-12-31

A wavelet characterization for weighted Hardy Spaces

Sijue Wu[1]

(1) New York University, USA

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 $H^{p_2}(\omega), 1 ≤ p_1 < p_2 < \infty$.

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Wu Sijue: A wavelet characterization for weighted Hardy Spaces. Rev. Mat. Iberoam. 8 (1992), 329-349. doi: 10.4171/RMI/127