Le commutateur entre la multiplication par une fonction et une transformation des martingales d’un type certain est un opérateur borné sur , , si et seulement si la fonction appartient à BMO. C’est une analogie pour martingales d’un résultat de Coifman, Rochberg et Weiss.
The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on , , if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.
@article{AIF_1981__31_1_265_0, author = {Janson, Svante}, title = {BMO and commutators of martingale transforms}, journal = {Annales de l'Institut Fourier}, pages = {265--270}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {31}, number = {1}, year = {1981}, doi = {10.5802/aif.827}, mrnumber = {83b:60038}, zbl = {0437.42015}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.827/} }
TY - JOUR AU - Janson, Svante TI - BMO and commutators of martingale transforms JO - Annales de l'Institut Fourier PY - 1981 SP - 265 EP - 270 VL - 31 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.827/ DO - 10.5802/aif.827 LA - en ID - AIF_1981__31_1_265_0 ER -
Janson, Svante. BMO and commutators of martingale transforms. Annales de l'Institut Fourier, Tome 31 (1981) no. 1, pp. 265-270. doi : 10.5802/aif.827. http://archive.numdam.org/articles/10.5802/aif.827/
[1] Factorization theorems for Hardy spaces in several variables, Ann. Math., 103 (1976), 611-635. | MR | Zbl
, and ,[2] Hp-spaces of several variables, Acta Math., 129 (1972), 137-193. | MR | Zbl
and ,[3] Characterizations of H1 by singular integral transforms on martingales and Rn, Math. Scand., 41 (1977), 140-152. | MR | Zbl
,[4] Mean oscillation and commutators of singular integral operators, Ark. Mat., 16 (1978), 263-270. | MR | Zbl
,[5] Compactness of operators of Hankel type, Tôhoku Math. J., 30 (1978), 163-171. | MR | Zbl
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