Comptes Rendus
no. 12
Harmonic Analysis/Functional Analysis
BMO is the intersection of two translates of dyadic BMO
[BMO est l'intersection de deux translatés de BMO dyadique]

Présenté par : Gilles Pisier

Tao Mei1
1 Mathematics Department, Texas A&M University, College Station, TX 77843, USA
Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 1003-1006.

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

∥ϕ∥ BMO (𝕋) ⋍∥ϕ∥ BMO 𝒟 (𝕋) +∥ϕ(·-2δπ)∥ BMO 𝒟 (𝕋) ,∀ϕ∈ BMO (𝕋).

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

∥ϕ∥ BMO (𝕋) ⋍∥ϕ∥ BMO 𝒟 (𝕋) +∥ϕ(·-2δπ)∥ BMO 𝒟 (𝕋) ,∀ϕ∈ BMO (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/

[1] J.B. Garnett; P.W. Jones BMO from dyadic BMO, Pacific J. Math., Volume 99 (1982) no. 2, pp. 351-371

[2] J.B. Garnett Bounded Analytic Functions, Pure Appl. Math., 96, Academic Press, New York, 1981

[3] T. Mei, Operator valued Hardy spaces, Preprint

[4] S. Petermichl Dyadic shifts and a logarithmic estimate for Hankel operator with matrix symbol, C. R. Acad. Sci. Paris, Ser. I, Volume 330 (2000), pp. 455-460

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