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dc.contributor.authorLi, K.
dc.contributor.authorPérez, C.
dc.contributor.authorRivera-Ríos, I.P.
dc.contributor.authorRoncal, L.
dc.date.accessioned2018-08-23T11:55:43Z
dc.date.available2018-08-23T11:55:43Z
dc.date.issued2018-08-17
dc.identifier.issn1050-6926
dc.identifier.urihttp://hdl.handle.net/20.500.11824/843
dc.description.abstractIn this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index $B_{(n-1)/2}$. More precisely, we prove qualitative and quantitative versions of Coifman--Fefferman type inequalities and their vector-valued extensions, weighted $A_p-A_\infty$ strong and weak type inequalities for $1<p<\infty$, and $A_1-A_\infty$ type weak $(1,1)$ estimates. Moreover, Fefferman--Stein type inequalities are obtained, proving in this way a conjecture raised by the second-named author in the 90's. As a corollary, we obtain the weighted $A_1-A_\infty$ type estimates. Finally, we study rough homogenous singular integrals with a kernel involving a function $\Omega\in L^q(\mathbb{S}^{n-1})$, $1<q<\infty$, and provide Fefferman--Stein inequalities too. The arguments used for our proofs combine several tools: a recent sparse domination result by Conde--Alonso et al. \cite{CACDPO}, results by the first author in \cite{L}, suitable adaptations of Rubio de Francia algorithm, the extrapolation theorems for $A_{\infty}$ weights \cite{CMP,CGMP} and ideas contained in previous works by A. Seeger in \cite{S} and D. Fan and S. Sato \cite{FS}.en_US
dc.description.sponsorshipJuan de la Cierva - Formaci\'on 2015 FJCI-2015-24547. BBVA Foundationen_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectrough operatorsen_US
dc.subjectweightsen_US
dc.subjectFefferman-Stein inequalitiesen_US
dc.subjectsparse operatorsen_US
dc.subjectRubio de Francia algorithmen_US
dc.titleWeighted norm inequalities for rough singular integral operatorsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.relation.projectIDES/1PE/SEV-2013-0323en_US
dc.relation.projectIDES/1PE/MTM2017-82160-C2-1-Pen_US
dc.relation.projectIDEUS/BERC/BERC.2018-2021en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleJournal of Geometric Analysisen_US


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