To cite this record: http://ddd.uab.cat/record/85170
Sharp norm inequalities for commutators of classical operators
Cruz-Uribe, David
SFO
Moen, Kabe

 Date: 2012 Abstract: 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. Rights: Tots els drets reservats Document type: article ; recerca ; publishedVersion Subject: Commutators ; Two-weight inequalities ; Sharp weighted bounds Published in: Publicacions matemàtiques, Vol. 56, Núm. 1 ( 2012) , p. 147-190, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_56112_06

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