85170
20150330143141.0
artpubuab
driver
oai:ddd.uab.cat:85170
doi
10.5565/PUBLMAT_56112_06
articleid
02141493v56n1p147
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.
info:eu-repo/semantics/restrictedAccess
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http://www.europeana.eu/rights/rr-f/
Anglès.
recerca
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/pub/pubmat/02141493v56n1/pubmat_a2012v56n1p147.pdf
0147
190
1
56
02141493v56n1
2012
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