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

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...

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Detalles Bibliográficos
Autores: Bakas, O., Pott, S., Rodríguez-López, S., Sola, A.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1582
Acceso en línea:http://hdl.handle.net/20.500.11824/1582
https://dx.doi.org/10.4310/ARKIV.2022.v60.n2.a2
Access Level:acceso abierto
Palabra clave:Maximal function
Real Hardy spaces
Orlicz spaces
Haar wavelets
Descripción
Sumario: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.