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dc.contributor.authorGonzález-Pérez, Adrián M. ; Junge, Marius ;Parcet, Javier-
dc.date.accessioned2021-11-05T09:50:03Z-
dc.date.available2021-11-05T09:50:03Z-
dc.date.issued2021-
dc.identifierdoi: 10.1090/memo/1334-
dc.identifierissn: 0065-9266-
dc.identifier.citationMEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY 272: 1- 87 (2021)-
dc.identifier.urihttp://hdl.handle.net/10261/253748-
dc.description.abstractIn this paper, we establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes¿ pseudodifferential calculus for rotation algebras, thanks to a new form of Calder¿on-Zygmund theory over these spaces which crucially incorporates nonconvolution kernels. We deduce Lp-boundedness and Sobolev p-estimates for regular, exotic and forbidden symbols in the expected ranks. In the L2 level both Calder¿on-Vaillancourt and Bourdaud theorems for exotic and forbidden symbols are also generalized to the quantum setting. As a basic application of our methods, we prove Lp-regularity of solutions for elliptic PDEs-
dc.description.sponsorshipA. Gonz ́alez-P ́erez was partially supported by European Research Council Consolidator Grant 614195. M. Junge was partially supported by the NSF DMS-1501103. J. Parcet was partially supported by European Research Council Starting Grant 256997 and CSIC Grant PIE 201650E030. All authors are also supported in part by ICMAT Severo Ochoa Grant SEV-2015-0554 (Spain).-
dc.languageeng-
dc.publisherAmerican Mathematical Society-
dc.relationMINECO/ICTI2013-2016/SEV-2015-0554-
dc.relationinfo:eu-repo/grantAgreement/EC/FP7/12345-
dc.relation.isversionofPreprint-
dc.rightsopenAccess-
dc.titleSingular integrals in quantum Euclidean spaces-
dc.typeartículo-
dc.relation.publisherversionhttp://dx.doi.org/10.1090/memo/1334-
dc.date.updated2021-11-05T09:50:03Z-
dc.contributor.funderMinisterio de Ciencia, Innovación y Universidades (España)-
dc.contributor.funderEuropean Commission-
dc.relation.csic-
dc.identifier.funderhttp://dx.doi.org/10.13039/501100000780es_ES
dc.type.coarhttp://purl.org/coar/resource_type/c_6501es_ES
item.grantfulltextopen-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.cerifentitytypePublications-
item.fulltextWith Fulltext-
item.openairetypeartículo-
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