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arXiv · 2012.02872

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

Odysseas Bakas·Sandra Pott·Salvador Rodríguez-López·Alan Sola
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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.

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Odysseas Bakas, Sandra Pott, Salvador Rodríguez-López, Alan Sola. 2020-12-04. Notes on $H^{\log} $: structural properties, dyadic variants, and bilinear $H^1$-$BMO$ mappings. https://arxiv.org/abs/2012.02872

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