no. 1
BMO and commutators of martingale transforms
Annales de l'Institut Fourier, Tome 31 (1981) no. 1, pp. 265-270.

Le commutateur entre la multiplication par une fonction et une transformation des martingales d’un type certain est un opérateur borné sur L p , 1<p<∞, 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 L p , 1<p<∞, if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.

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     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},
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     zbl = {0437.42015},
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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://www.numdam.org/articles/10.5802/aif.827/

[1] R.R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. Math., 103 (1976), 611-635. | MR | Zbl

[2] C. Fefferman and E.M. Stein, Hp-spaces of several variables, Acta Math., 129 (1972), 137-193. | MR | Zbl

[3] S. Janson, Characterizations of H1 by singular integral transforms on martingales and Rn, Math. Scand., 41 (1977), 140-152. | MR | Zbl

[4] S. Janson, Mean oscillation and commutators of singular integral operators, Ark. Mat., 16 (1978), 263-270. | MR | Zbl

[5] A. Uchiyama, Compactness of operators of Hankel type, Tôhoku Math. J., 30 (1978), 163-171. | MR | Zbl

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