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 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).

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).

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
@article{CRMATH_2003__336_12_1003_0,
     author = {Tao Mei},
     title = {BMO is the intersection of two translates of dyadic {BMO}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1003--1006},
     publisher = {Elsevier},
     volume = {336},
     number = {12},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00234-6},
     language = {en},
}
TY  - JOUR
AU  - Tao Mei
TI  - BMO is the intersection of two translates of dyadic BMO
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 1003
EP  - 1006
VL  - 336
IS  - 12
PB  - Elsevier
DO  - 10.1016/S1631-073X(03)00234-6
LA  - en
ID  - CRMATH_2003__336_12_1003_0
ER  - 
%0 Journal Article
%A Tao Mei
%T BMO is the intersection of two translates of dyadic BMO
%J Comptes Rendus. Mathématique
%D 2003
%P 1003-1006
%V 336
%N 12
%I Elsevier
%R 10.1016/S1631-073X(03)00234-6
%G en
%F CRMATH_2003__336_12_1003_0
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

Cité par Sources :

Commentaires - Politique