Global Stein theorem on Hardy spaces

A. Bonami; S. Grellier; B. F. Sehba

doi:10.1007/s10476-024-00003-2

Global Stein theorem on Hardy spaces

A. Bonami
, S. Grellier
, B. F. Sehba

Department of Mathematics

Université d’Orléans

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

1 Citation (Scopus)

Abstract

Let f be an integrable function which has integral 0 on Rⁿ.What is the largest condition on |f| that guarantees that f is in the Hardy spaceH¹(Rⁿ)? When f is compactly supported, it is well-known that the largest conditionon |f| is the fact that |f|∈LlogL(Rⁿ). We consider the same kind ofproblem here, but without any condition on the support. We do so for H¹(Rⁿ),as well as for the Hardy space H_log(Rⁿ) which appears in the study of pointwiseproducts of functions in H¹(Rⁿ) and in its dual BMO.

Original language	English
Pages (from-to)	79-99
Number of pages	21
Journal	Analysis Mathematica
Volume	50
Issue number	1
DOIs	https://doi.org/10.1007/s10476-024-00003-2
Publication status	Published - Mar 2024

Keywords

42B25
42B30
46E30
Hardy space
Hardy-Musielak space
Stein theorem

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10.1007/s10476-024-00003-2

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T1 - Global Stein theorem on Hardy spaces

AU - Bonami, A.

AU - Grellier, S.

AU - Sehba, B. F.

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Akadémiai Kiadó, Budapest, Hungary 2024.

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N2 - Let f be an integrable function which has integral 0 on Rn.What is the largest condition on |f| that guarantees that f is in the Hardy spaceH1(Rn)? When f is compactly supported, it is well-known that the largest conditionon |f| is the fact that |f|∈LlogL(Rn). We consider the same kind ofproblem here, but without any condition on the support. We do so for H1(Rn),as well as for the Hardy space Hlog(Rn) which appears in the study of pointwiseproducts of functions in H1(Rn) and in its dual BMO.

AB - Let f be an integrable function which has integral 0 on Rn.What is the largest condition on |f| that guarantees that f is in the Hardy spaceH1(Rn)? When f is compactly supported, it is well-known that the largest conditionon |f| is the fact that |f|∈LlogL(Rn). We consider the same kind ofproblem here, but without any condition on the support. We do so for H1(Rn),as well as for the Hardy space Hlog(Rn) which appears in the study of pointwiseproducts of functions in H1(Rn) and in its dual BMO.

KW - 42B25

KW - 42B30

KW - 46E30

KW - Hardy space

KW - Hardy-Musielak space

KW - Stein theorem

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DO - 10.1007/s10476-024-00003-2

M3 - Article

AN - SCOPUS:85188281393

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VL - 50

SP - 79

EP - 99

JO - Analysis Mathematica

JF - Analysis Mathematica

IS - 1

ER -

Global Stein theorem on Hardy spaces

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