eng
Sharp norm inequalities for commutators of classical operators
Cruz-Uribe, David
SFO
Moen, Kabe
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
2012
Commutators
Two-weight inequalities
Sharp weighted bounds
Publicacions matemàtiques ; Vol. 56, Núm. 1 ( 2012), p. 147-190
http://ddd.uab.cat/record/85170
oai:ddd.uab.cat:85170
10.5565/PUBLMAT_56112_06
02141493v56n1p147
Tots els drets reservats
http://www.europeana.eu/rights/rr-f/
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.
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