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

Wael Abu-Shammala; Ji-Liang Shiu; Alberto Torchinsky

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

Functional Analysis 2007-05-23 v2 Classical Analysis and ODEs

Authors: Wael Abu-Shammala , Ji-Liang Shiu , Alberto Torchinsky

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 $(R)$ .

Keywords

hardy space bmo dyadic hardy space two-sided hardy space bounded linear operator banach space continuous extension

Cite

@article{arxiv.math/0510280,
  title  = {Characterizations of the Hardy Space $H^1$ and BMO},
  author = {Wael Abu-Shammala and Ji-Liang Shiu and Alberto Torchinsky},
  journal= {arXiv preprint arXiv:math/0510280},
  year   = {2007}
}

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33 pages

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

Abstract

Keywords

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