Sharp norm inequalities for commutators of classical operators
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Autores: David Cruz-Uribe
, Kabe Moen
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 56, Nº 1, 2012, págs. 147-190
- Idioma: inglés
- DOI: 10.5565/publmat_56112_06
- Enlaces
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Resumen
We prove several sharp weighted norm inequalities for commutators of classical operators in harmonic analysis. We nd sucient 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.
