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dc.contributor.authorLi, K.
dc.contributor.authorMartikainen, H.
dc.contributor.authorVuorinen, E.
dc.date.accessioned2019-12-09T08:43:43Z
dc.date.available2019-12-09T08:43:43Z
dc.date.issued2019-10
dc.identifier.issn0021-7824
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1050
dc.description.abstractWe develop a wide general theory of bilinear bi-parameter singular integrals $T$. This includes general Calder\'on--Zygmund type principles in the bilinear bi-parameter setting: easier bounds, like estimates in the Banach range, imply boundedness in the full bilinear range $L^p \times L^q \to L^r$, $1/p + 1/q = 1/r$, $1 < p,q \le \infty$, $1/2 < r < \infty$, weighted estimates, mixed-norm estimates, and so on. We build this Calder\'on--Zygmund theory using the very useful perspective of dyadic representation theorems that hold under testing conditions. New weighted estimates are developed and used effectively throughout. We also develop commutator decompositions and use them to show estimates in the full range for commutators and iterated commutators, like $[b_1,T]_1$ and $[b_2, [b_1, T]_1]_2$, where $b_1$ and $b_2$ are little BMO functions. Our commutator method contains several novelties -- one is that the new method can be used to simplify and improve linear commutator proofs, even in the two-weight Bloom setting. We also quickly show commutator lower bounds by using and developing the recent median method.en_US
dc.description.sponsorshipJuan de la Cierva - Formaci\'on 2015 [FJCI-2015-24547]; BCAM Severo Ochoa excellence accreditation [SEV-2013-0323]; Academy of Finland [294840, 306901, 307333]; University of Helsinki three-year research grant [75160010]en_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.subjectCalder\'on--Zygmund operatorsen_US
dc.subjectbi-parameter analysisen_US
dc.subjectbilinear analysisen_US
dc.subjectcommutatorsen_US
dc.titleBilinear Calderón--Zygmund theory on product spacesen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.relation.publisherversionhttps://doi.org/10.1016/j.matpur.2019.10.007en_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 des Math\'ematiques Pures et Appliqu\'eesen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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