Sharp norm inequalities for commutators of classical operators
Cruz-Uribe, David (Trinity College (Hartford, Estats Units d'Amèrica). Department of Mathematics)
Moen, Kabe (University of Alabama. Department of Mathematics)

Data:	2012
Resum:	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.
Ajuts:	Ministerio de Ciencia e Innovación MTM2009-08934
Drets:	Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Commutators ; Two-weight inequalities ; Sharp weighted bounds
Publicat a:	Publicacions matemàtiques, Vol. 56, Núm. 1 ( 2012) , p. 147-190, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/248364
DOI: 10.5565/PUBLMAT_56112_06

44 p, 543.4 KB

El registre apareix a les col·leccions:
Articles > Articles publicats > Publicacions matemàtiques
Articles > Articles de recerca