Harmonic Analysis/Functional Analysis
BMO is the intersection of two translates of dyadic BMO
Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 1003-1006.

Let 𝕋 be the unit circle on 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, we have

ϕ BMO (𝕋) ϕ BMO 𝒟 (𝕋) +ϕ(·-2δπ) BMO 𝒟 (𝕋) ,ϕ BMO (𝕋).

Soit 𝕋 le cercle unité dans 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, 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).

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DOI: 10.1016/S1631-073X(03)00234-6
Mei, Tao 1

1 Mathematics Department, Texas A&M University, College Station, TX 77843, USA
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Mei, Tao. 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. http://www.numdam.org/articles/10.1016/S1631-073X(03)00234-6/

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

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

[4] Petermichl, S. 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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