Comptes Rendus
Harmonic Analysis/Functional Analysis
BMO is the intersection of two translates of dyadic BMO
[BMO est l'intersection de deux translatés de BMO dyadique]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 1003-1006.

Soit 𝕋 le cercle unité dans 2. On note BMO(𝕋) l'espace BMO classique et l'on note BMO𝒟(𝕋) l'espace BMO dyadique usuel sur 𝕋. Pour certaines valeurs de δ, nous montrons que l'espace BMO(𝕋) coı̈ncide avec l'intersection de BMO𝒟(𝕋) et du translaté par δ de BMO𝒟(𝕋), en d'autres termes que l'on a

ϕBMO(𝕋)ϕBMO𝒟(𝕋)+ϕ(·-2δπ)BMO𝒟(𝕋),ϕBMO(𝕋).

Let 𝕋 be the unit circle on 2. Denote by BMO(𝕋) the classical BMO space and denote by BMO𝒟(𝕋) the usual dyadic BMO space on 𝕋. Then, for suitably chosen δ, we have

ϕBMO(𝕋)ϕBMO𝒟(𝕋)+ϕ(·-2δπ)BMO𝒟(𝕋),ϕBMO(𝕋).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00234-6

Tao Mei 1

1 Mathematics Department, Texas A&M University, College Station, TX 77843, USA
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Tao Mei. BMO is the intersection of two translates of dyadic BMO. Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 1003-1006. doi : 10.1016/S1631-073X(03)00234-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00234-6/

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