Notes on Hlog: structural properties, dyadic variants, and bilinear H1-BMO mappings

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

doi:10.4310/ARKIV.2022.v60.n2.a2

Notes on H^log: structural properties, dyadic variants, and bilinear H¹-BMO mappings

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

Mathematics (Faculty of Sciences)

Research output: Contribution to journal › Article › peer-review

Abstract

This article is devoted to a study of the Hardy space H^log(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 H¹ 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.

Original language	English
Pages (from-to)	231-275
Number of pages	45
Journal	Arkiv for Matematik
Volume	60
Issue number	2
DOIs	https://doi.org/10.4310/ARKIV.2022.v60.n2.a2
Publication status	Published - 2022

Subject classification (UKÄ)

Mathematical Analysis

Free keywords

and phrases: maximal function
Haar wavelets
Orlicz spaces
real Hardy spaces

Access to Document

10.4310/ARKIV.2022.v60.n2.a2

Cite this

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abstract = "This article is devoted to a study of the Hardy space Hlog(Rd) 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 H1 and a function in BMO to distributions that belong to Hlog based on dyadic paraproducts. We also point out analogues of classical results of Hardy-Littlewood, Zygmund, and Stein for Hlog and related Musielak-Orlicz spaces.",

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AU - Sola, Alan

PY - 2022

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AB - This article is devoted to a study of the Hardy space Hlog(Rd) 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 H1 and a function in BMO to distributions that belong to Hlog based on dyadic paraproducts. We also point out analogues of classical results of Hardy-Littlewood, Zygmund, and Stein for Hlog and related Musielak-Orlicz spaces.

KW - and phrases: maximal function

KW - Haar wavelets

KW - Orlicz spaces

KW - real Hardy spaces

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