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dc.contributor.authorEriksson-Bique, Sylvester
dc.contributor.authorRajala, Tapio
dc.contributor.authorSoultanis, Elefterios
dc.date.accessioned2023-07-07T10:26:40Z
dc.date.available2023-07-07T10:26:40Z
dc.date.issued2024
dc.identifier.citationEriksson-Bique, S., Rajala, T., & Soultanis, E. (2024). Tensorization of quasi-Hilbertian Sobolev spaces. <i>Revista Matematica Iberoamericana</i>, <i>40</i>(2), 565-580. <a href="https://doi.org/10.4171/rmi/1433" target="_blank">https://doi.org/10.4171/rmi/1433</a>
dc.identifier.otherCONVID_183829120
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/88306
dc.description.abstractThe tensorization problem for Sobolev spaces asks for a characterization of how the Sobolev space on a product metric measure space X Y can be determined from its factors. We show that two natural descriptions of the Sobolev space from the literature coincide, W 1;2.X Y / D J 1;2.X; Y /, thus settling the tensorization problem for Sobolev spaces in the case p D 2, when X and Y are infinitesimally quasi-Hilbertian, i.e., the Sobolev space W 1;2 admits an equivalent renorming by a Dirichlet form. This class includes in particular metric measure spaces X; Y of finite Hausdorff dimension as well as infinitesimally Hilbertian spaces. More generally, for p 2 .1;1/ we obtain the norm-one inclusion kf kJ1;p.X;Y / kf kW 1;p.XY / and show that the norms agree on the algebraic tensor product W 1;p.X / ˝ W 1;p.Y / W 1;p.X Y /: When p D 2 and X and Y are infinitesimally quasi-Hilbertian, standard Dirichlet forms theory yields the density of W 1;2.X / ˝ W 1;2.Y / in J 1;2.X; Y /, thus implying the equality of the spaces. Our approach raises the question of the density of W 1;p.X / ˝ W 1;p.Y / in J 1;p.X; Y / in the general case.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherEMS Press
dc.relation.ispartofseriesRevista Matematica Iberoamericana
dc.rightsCC BY 4.0
dc.subject.otherSobolev spaces
dc.subject.othertensorization
dc.subject.otherDirichlet forms
dc.subject.othermetric measure spaces
dc.subject.otheranalysis on metric spaces
dc.subject.otherminimal upper gradient
dc.titleTensorization of quasi-Hilbertian Sobolev spaces
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202307074433
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineAnalyysin ja dynamiikan tutkimuksen huippuyksikköfi
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineAnalysis and Dynamics Research (Centre of Excellence)en
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange565-580
dc.relation.issn0213-2230
dc.relation.numberinseries2
dc.relation.volume40
dc.type.versionpublishedVersion
dc.rights.copyright© 2023 Real Sociedad Matemática Española
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber314789
dc.subject.ysofunktionaalianalyysi
dc.subject.ysopotentiaaliteoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p17780
jyx.subject.urihttp://www.yso.fi/onto/yso/p18911
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.4171/rmi/1433
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundinginformationS. Eriksson-Bique was partially supported by the Finnish Academy grant no. 345005. T. Rajala was partially supported by the Finnish Academy grant no. 314789.
dc.type.okmA1


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