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Regularity versus smoothness of measures
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dc.contributor.author | Fraser, Jonathan | |
dc.contributor.author | Troscheit, Sascha | |
dc.date.accessioned | 2021-03-10T16:30:16Z | |
dc.date.available | 2021-03-10T16:30:16Z | |
dc.date.issued | 2021-07-31 | |
dc.identifier | 273170207 | |
dc.identifier | 5822beb9-bd05-482a-9d30-17bf6af33114 | |
dc.identifier | 000680656700001 | |
dc.identifier | 85112657949 | |
dc.identifier.citation | Fraser , 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.2021.311.257 | en |
dc.identifier.issn | 0030-8730 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/98487773 | |
dc.identifier.uri | https://hdl.handle.net/10023/21596 | |
dc.description | Funding: 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.abstract | The 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.extent | 17 | |
dc.format.extent | 404718 | |
dc.language.iso | eng | |
dc.relation.ispartof | Pacific Journal of Mathematics | en |
dc.subject | Assouad dimension | en |
dc.subject | Assouad spectrum | en |
dc.subject | Lower dimension | en |
dc.subject | Lower spectrum | en |
dc.subject | Lp-spaces | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Regularity versus smoothness of measures | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.2140/pjm.2021.311.257 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/1912.07292 | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
dc.identifier.grantnumber | RPG-2019-034 | en |
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