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dc.contributor.authorLi, K.
dc.contributor.authorMartikainen, H.
dc.contributor.authorVuorinen, E.
dc.date.accessioned2019-03-15T09:18:41Z
dc.date.available2019-03-15T09:18:41Z
dc.date.issued2019-03-14
dc.identifier.issn1073-7928
dc.identifier.urihttp://hdl.handle.net/20.500.11824/950
dc.description.abstractUtilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ is a bi-parameter singular integral satisfying the assumptions of the bi-parameter representation theorem, then $$ \| [b_k,\cdots[b_2, [b_1, T]]\cdots]\|_{L^p(\mu) \to L^p(\lambda)} \lesssim_{[\mu]_{A_p}, [\lambda]_{A_p}} \prod_{i=1}^k\|b_i\|_{{\rm{bmo}}(\nu^{\theta_i})} , $$ where $p \in (1,\infty)$, $\theta_i \in [0,1]$, $\sum_{i=1}^k\theta_i=1$, $\mu, \lambda \in A_p$, $\nu := \mu^{1/p}\lambda^{-1/p}$. Here $A_p$ stands for the bi-parameter weights in $\mathbb R^n \times \mathbb R^m$ and ${\rm{bmo}}(\nu)$ is a suitable weighted little BMO space. We also simplify the proof of the known first order case.en_US
dc.description.sponsorshipJuan de la Cierva - Formación 2015 FJCI-2015-24547, BCAM Severo Ochoa excellence accreditation SEV-2013-0323en_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.subjectrepresentation theoremsen_US
dc.subjectiterated commutatorsen_US
dc.subjectBloom's inequalityen_US
dc.titleBloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutatorsen_US
dc.typeinfo:eu-repo/semantics/articleen_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.titleInternational Mathematics Research Noticesen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España