Odysseas Bakas, Sandra Pott, Salvador Rodríguez-López, Alan Sola
Published 2020-12-04Version 1
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.
Comments: This article supersedes and extends a previous article arXiv:1905.13477
Boundedness of dyadic paraproducts on matrix weighted $L^p$
Norm of the Hausdorff operator on the real Hardy space $H^1(\mathbb R)$
Unitary matrix functions, wavelet algorithms, and structural properties of wavelets
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