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A wavelet characterization for weighted Hardy spaces. (English) Zbl 0769.42011

Summary: 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 \(\text{BMO}_ \omega\). Moreover, we obtain interpolation between \(A_ \infty\)-weighted Hardy spaces \(H^{p_ 1}(\omega)\) and \(H^{p_ 2}(\omega)\), \(1\leq p_ 1<p_ 2<\infty\).

MSC:

42B30 \(H^p\)-spaces
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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