dc.contributor.author Hytönen, T.P. dc.contributor.author Roncal, L. dc.contributor.author Tapiola, O. dc.date info:eu-repo/date/embargoEnd/2018-02-28 en_US dc.date.accessioned 2017-04-08T12:31:44Z dc.date.available 2017-04-08T12:31:44Z dc.date.issued 2017-03-11 dc.identifier.issn 0021-2172 dc.identifier.uri http://hdl.handle.net/20.500.11824/660 dc.description.abstract We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound that is quadratic in the $A_2$ constant $[w]_{A_2}$. We do not know if this is sharp, but it is the best known quantitative result for this class of operators. The proof relies on a classical decomposition of these operators into smooth pieces, for which we use a quantitative elaboration of Lacey's dyadic decomposition of Dini-continuous operators: the dependence of constants on the Dini norm of the kernels is crucial to control the summability of the series expansion of the rough operator. We conclude with applications and conjectures related to weighted bounds for powers of the Beurling transform. en_US dc.description.sponsorship MTM2015-65888-C04-4-P from Spanish Government and the mobility grant "José Castillejo" number CAS14/00037 from Ministerio de Educación, Cultura y Deporte of Spain en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.title Quantitative weighted estimates for rough homogeneous singular integrals en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1007/s11856-017-1462-6 dc.relation.publisherversion http://link.springer.com/article/10.1007/s11856-017-1462-6 en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/embargoedAccess en_US dc.type.hasVersion info:eu-repo/semantics/publishedVersion en_US dc.journal.title Israel Journal of Mathematics en_US
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