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

Bakas, Odysseas LU ; Pott, Sandra LU ; Rodríguez-López, Salvador and Sola, Alan (2022) In Arkiv for Matematik 60(2). p.231-275
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.

Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
and phrases: maximal function, Haar wavelets, Orlicz spaces, real Hardy spaces
in
Arkiv for Matematik
volume
60
issue
2
pages
45 pages
publisher
Springer
external identifiers
  • scopus:85140486630
ISSN
0004-2080
DOI
10.4310/ARKIV.2022.v60.n2.a2
language
English
LU publication?
yes
id
93e1cb2d-d9f7-4da0-b875-86376d9e17dc
date added to LUP
2022-12-19 14:35:11
date last changed
2022-12-19 14:35:11
@article{93e1cb2d-d9f7-4da0-b875-86376d9e17dc,
  abstract     = {{<p>This article is devoted to a study of the Hardy space H<sup>log</sup>(R<sup>d</sup>) 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<sup>1</sup> and a function in BMO to distributions that belong to H<sup>log</sup> based on dyadic paraproducts. We also point out analogues of classical results of Hardy-Littlewood, Zygmund, and Stein for H<sup>log</sup> and related Musielak-Orlicz spaces.</p>}},
  author       = {{Bakas, Odysseas and Pott, Sandra and Rodríguez-López, Salvador and Sola, Alan}},
  issn         = {{0004-2080}},
  keywords     = {{and phrases: maximal function; Haar wavelets; Orlicz spaces; real Hardy spaces}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{231--275}},
  publisher    = {{Springer}},
  series       = {{Arkiv for Matematik}},
  title        = {{Notes on H<sup>log</sup> : structural properties, dyadic variants, and bilinear H<sup>1</sup>-BMO mappings}},
  url          = {{http://dx.doi.org/10.4310/ARKIV.2022.v60.n2.a2}},
  doi          = {{10.4310/ARKIV.2022.v60.n2.a2}},
  volume       = {{60}},
  year         = {{2022}},
}