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

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.

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.

Janson, Svante. BMO and commutators of martingale transforms. Annales de l'Institut Fourier, Volume 31 (1981) no. 1, pp. 265-270. doi: 10.5802/aif.827
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[1] R.R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. Math., 103 (1976), 611-635. | Zbl | MR

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

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

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

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

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