dc.contributor.author | Eriksson-Bique, Sylvester | |
dc.contributor.author | Rajala, Tapio | |
dc.contributor.author | Soultanis, Elefterios | |
dc.date.accessioned | 2023-07-07T10:26:40Z | |
dc.date.available | 2023-07-07T10:26:40Z | |
dc.date.issued | 2024 | |
dc.identifier.citation | Eriksson-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.other | CONVID_183829120 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/88306 | |
dc.description.abstract | The 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.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | EMS Press | |
dc.relation.ispartofseries | Revista Matematica Iberoamericana | |
dc.rights | CC BY 4.0 | |
dc.subject.other | Sobolev spaces | |
dc.subject.other | tensorization | |
dc.subject.other | Dirichlet forms | |
dc.subject.other | metric measure spaces | |
dc.subject.other | analysis on metric spaces | |
dc.subject.other | minimal upper gradient | |
dc.title | Tensorization of quasi-Hilbertian Sobolev spaces | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202307074433 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Analyysin ja dynamiikan tutkimuksen huippuyksikkö | fi |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Analysis and Dynamics Research (Centre of Excellence) | en |
dc.contributor.oppiaine | Mathematics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 565-580 | |
dc.relation.issn | 0213-2230 | |
dc.relation.numberinseries | 2 | |
dc.relation.volume | 40 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © 2023 Real Sociedad Matemática Española | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 314789 | |
dc.subject.yso | funktionaalianalyysi | |
dc.subject.yso | potentiaaliteoria | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p17780 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p18911 | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.4171/rmi/1433 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | Academy Project, AoF | en |
jyx.fundingprogram | Akatemiahanke, SA | fi |
jyx.fundinginformation | S. 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.okm | A1 | |