Notes on $H^{\log} $: structural properties, dyadic variants, and bilinear $H^1$-$BMO$ mappings

Odysseas Bakas; Sandra Pott; Salvador Rodríguez-López; Alan Sola

Notes on $H^{\log} $: structural properties, dyadic variants, and bilinear $H^1$-$BMO$ mappings

Classical Analysis and ODEs 2022-11-01 v1

Authors: Odysseas Bakas , Sandra Pott , Salvador Rodríguez-López , Alan Sola

Abstract

This article is devoted to a study of the Hardy space $H^{\log} (\mathbb{R}^d)$ introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space $H^1$ and a function in $BMO$ to distributions that belong to $H^{\log}$ based on dyadic paraproducts. We also point out analogues of classical results of Hardy-Littlewood, Zygmund, and Stein for $H^{\log}$ and related Musielak-Orlicz spaces.

Keywords

hardy spaces bmo spaces

Cite

@article{arxiv.2012.02872,
  title  = {Notes on $H^{\log} $: structural properties, dyadic variants, and bilinear $H^1$-$BMO$ mappings},
  author = {Odysseas Bakas and Sandra Pott and Salvador Rodríguez-López and Alan Sola},
  journal= {arXiv preprint arXiv:2012.02872},
  year   = {2022}
}

Comments

This article supersedes and extends a previous article arXiv:1905.13477

Notes on $H^{\log} $: structural properties, dyadic variants, and bilinear $H^1$-$BMO$ mappings

Abstract

Keywords

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