BMO is the intersection of two translates of dyadic BMO

Tao Mei

doi:10.1016/S1631-073X(03)00234-6

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 Mei ¹

¹ Mathematics Department, Texas A&M University, College Station, TX 77843, USA

Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 1003-1006.

Abstract (VO)
Résumé

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 $δ \in ℝ,$ we have

{∥ ϕ ∥}_{BMO (𝕋)} ⋍ {∥ ϕ ∥}_{{BMO}_{𝒟} (𝕋)} + {∥ ϕ (\cdot - 2 δ π) ∥}_{{BMO}_{𝒟} (𝕋)}, \forall ϕ \in BMO (𝕋) .

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 $δ \in ℝ$ , 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 (\cdot - 2 δ π) ∥}_{{BMO}_{𝒟} (𝕋)}, \forall ϕ \in BMO (𝕋) .

Reçu le : 2003-02-24
Accepté le : 2003-04-29
Publié le : 2003-06-11

DOI : 10.1016/S1631-073X(03)00234-6

Affiliations des auteurs :

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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