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

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

2005-10-13

arxiv.org/abs/math/0510280v2

Mathematics

Functional Analysis

33 pages

Scientific paper

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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