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Regularity versus smoothness of measures

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dc.contributor.authorFraser, Jonathan
dc.contributor.authorTroscheit, Sascha
dc.date.accessioned2021-03-10T16:30:16Z
dc.date.available2021-03-10T16:30:16Z
dc.date.issued2021-07-31
dc.identifier.citationFraser , J & Troscheit , S 2021 , ' Regularity versus smoothness of measures ' , Pacific Journal of Mathematics , vol. 311 , no. 2 , pp. 257–275 . https://doi.org/10.2140/pjm.2021.311.257en
dc.identifier.issn0030-8730
dc.identifier.otherPURE: 273170207
dc.identifier.otherPURE UUID: 5822beb9-bd05-482a-9d30-17bf6af33114
dc.identifier.otherORCID: /0000-0002-8066-9120/work/98487773
dc.identifier.otherWOS: 000680656700001
dc.identifier.otherScopus: 85112657949
dc.identifier.urihttps://hdl.handle.net/10023/21596
dc.descriptionFunding: JMF was financially supported by the EPSRC Standard Grant EP/R015104/1 and the Leverhulme Trust Research Project Grant RPG-2019-034. ST was initially supported by the AÖU Collaborative Grant 103öu6 [in part] and later by the Austrian Science Fund (FWF) Meitner Fellowship M-2813.en
dc.description.abstractThe Assouad and lower dimensions and dimension spectra quantify the regularity of a measure by considering the relative measure of concentric balls. On the other hand, one can quantify the smoothness of an absolutely continuous measure by considering the Lp norms of its density. We establish sharp relationships between these two notions. Roughly speaking, we show that smooth measures must be regular, but that regular measures need not be smooth.
dc.format.extent17
dc.language.isoeng
dc.relation.ispartofPacific Journal of Mathematicsen
dc.rightsCopyright © 2021 Pacific Journal of Mathematics. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.2140/pjm.2021.311.257.en
dc.subjectAssouad dimensionen
dc.subjectAssouad spectrumen
dc.subjectLower dimensionen
dc.subjectLower spectrumen
dc.subjectLp-spacesen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleRegularity versus smoothness of measuresen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.sponsorThe Leverhulme Trusten
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.2140/pjm.2021.311.257
dc.description.statusPeer revieweden
dc.identifier.urlhttps://arxiv.org/abs/1912.07292en
dc.identifier.grantnumberEP/R015104/1en
dc.identifier.grantnumberRPG-2019-034en


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