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Characterizations of the Hardy Space $H^1$ and BMO

Wael Abu-Shammala·Ji-Liang Shiu·Alberto Torchinsky
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Abstract

We describe the spaces $H^1(R)$ and BMO$(R)$ in terms of their closely related, simpler dyadic and two-sided counterparts. As a result of these characterizations we establish when a bounded linear operator defined on dyadic or two-sided $H^1(R)$ into a Banach space has a continuous extension to $H^1(R)$ and when a bounded linear operator that maps a Banach space into dyadic or two-sided BMO$(R)$ actually maps continuously into BMO$(R)$.

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Wael Abu-Shammala, Ji-Liang Shiu, Alberto Torchinsky. 2006-01-24. Characterizations of the Hardy Space $H^1$ and BMO. https://arxiv.org/abs/math/0510280

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