Geodesic
Weighted inequalities for commutators of one-sided singular integrals
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 1, pp. 83-101.

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We prove weighted inequalities for commutators of one-sided singular integrals (given by a Calder'on-Zygmund kernel with support in $(-\infty, 0)$) with BMO functions. We give the one-sided version of the results in C. Pérez, Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl., vol. 3 (6), 1997, pages 743–756 and C. Pérez, Endpoint estimates for commutators of singular integral operators, J. Funct. Anal., vol 128 (1), 1995, pages 163–185. We improve these results for one-sided singular integrals by putting in the right hand side of the inequalities a smaller operator and a wider class of weights.
Classification : 42B15, 42B25, 47G10
Keywords: one-sided weights; one-sided singular integrals 
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Lorente, M.; Riveros, M. S. Weighted inequalities for commutators of one-sided singular integrals. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 1, pp. 83-101. http://geodesic.mathdoc.fr/item/CMUC_2002__43_1_a7/