## 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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