85170 driver artpubuab oai:ddd.uab.cat:85170 articleid 02141493v56n1p147 doi 10.5565/PUBLMAT_56112_06 eng Cruz-Uribe, David Sharp norm inequalities for commutators of classical operators We prove several sharp weighted norm inequalities for commutators of classical operators in harmonic analysis. We found suffcient Ap-bump conditions on pairs of weights (u; v) such that [b; T], b 2 BMO and T a singular integral operator (such as the Hilbert or Riesz transforms), maps Lp(v) into Lp(u). Because of the added degree of singularity, the commutators require a \double log bump" as opposed to that of singular integrals, which only require single log bumps. For the fractional integral operator I we nd the sharp one-weight bound on [b; I ], b 2 BMO, in terms of the Ap;q constant of the weight. We also prove sharp two-weight bounds for [b; I ] analogous to those of singular integrals. We prove two-weight weak type inequalities for [b; T] and [b; I ] for pairs of factored weights. Finally we construct several examples showing our bounds are sharp. Article de fons Commutators Two-weight inequalities Sharp weighted bounds info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion SFO Moen, Kabe Vol. 56, Núm. 1 ( 2012), p. 147-190 Publicacions matemàtiques 0214-1493 44 556491 http://ddd.uab.cat/uab/pubmat/02141493v56n1/pubmat_a2012v56n1p147.pdf 0147 190 1 56 02141493v56n1 2012 ARTPUB UAB PUBMAT Tots els drets reservats http://www.europeana.eu/rights/rr-f/