dc.creator | Cruz Uribe, David | es |
dc.creator | Martell Berrocal, José María | es |
dc.creator | Pérez Moreno, Carlos | es |
dc.date.accessioned | 2016-06-15T10:16:49Z | |
dc.date.available | 2016-06-15T10:16:49Z | |
dc.date.issued | 2012-01-15 | |
dc.identifier.citation | Cruz Uribe, D. y Martell Berrocal, J.M. (2012). Sharp weighted estimates for classical operators. Advances in Mathematics, 229 (1), 408-441. | |
dc.identifier.issn | 0001-8708 | es |
dc.identifier.issn | 1090-2082 | es |
dc.identifier.uri | http://hdl.handle.net/11441/42328 | |
dc.description.abstract | We prove sharp one and two-weight norm inequalities for some of the classical operators of harmonic analysis: the Hilbert and Riesz transforms, the Beurling-Ahlfors operator, the maximal singular integrals associated to these operators, the dyadic square function and the vector-valued maximal operator. In the twoweight case we prove that these operators map L
p (v) into L p (u), 1 < p < ∞, provided that the pair (u, v) satisfies the Ap bump condition sup Q ku 1/pkA,Qkv −1/pkB,Q < ∞, where A¯ ∈ Bp0 and B¯ ∈ Bp. These conditions are known to be sharp in many cases and they characterize, in the scale of these Ap bump conditions, the corresponding two-weight norm inequalities for the Hardy-Littlewood maximal operator M: i.e., M : L p (v) −→ L p (u) and M : L p 0 (u 1−p 0 ) −→ L p (v 1−p 0 ). All of these results give positive answers to conjectures we made in. In the one-weight case we prove the sharp dependence on the Ap constant by finding the best value for the exponent α(p) such that kT fkLp(w) ≤ Cn,T [w] α(p)
Ap kfkLp(w) For the Hilbert transform, the Riesz transforms and the BeurlingAhlfors operator the sharp value of α(p) was found by Petermichl
and Volberg; their proofs used approximations by the dyadic Haar shift operators, Bellman function techniques, and twoweight norm inequalities. Our results for dyadic square functions and vector-valued maximal operators are new. All of our proofs again depend on dyadic approximation, but avoid Bellman functions and two-weight norm inequalities. We instead use a recent result due to A. Lerner [30] to estimate the oscillation of dyadic
operators. A key feature of our approach is that it will extend to any operator that can be approximated by Haar shift operators. | es |
dc.description.sponsorship | Faculty Research Committee and the Stewart-Dorwart Faculty Development Fund (Trinity College) | es |
dc.description.sponsorship | Ministerio de Ciencia e Innovación | es |
dc.description.sponsorship | Consejo Superior de Investigaciones Científicas | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Advances in Mathematics, 229 (1), 408-441. | es |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Ap weights | es |
dc.subject | Haar shift operators | es |
dc.subject | singular integral operators | es |
dc.subject | Hilbert transform | es |
dc.subject | Riesz transforms | es |
dc.subject | Beurling-Ahlfors operator | es |
dc.subject | dyadic square function | es |
dc.subject | vector-valued maximal operator | es |
dc.title | Sharp weighted estimates for classical operators | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | MTM2009-08934 | es |
dc.relation.projectID | MTM2007-60952 | es |
dc.relation.projectID | 200850I015 | es |
dc.relation.publisherversion | https://doi.org/10.1016/j.aim.2011.08.013 | |
dc.identifier.doi | 10.1016/j.aim.2011.08.013 | es |
idus.format.extent | 36 p. | es |
dc.journaltitle | Advances in Mathematics | es |
dc.publication.volumen | 229 | es |
dc.publication.issue | 1 | es |
dc.publication.initialPage | 408 | es |
dc.publication.endPage | 441 | es |
dc.relation.publicationplace | Amsterdam | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/42328 | |