Regularity versus smoothness of measures
MetadataShow full item record
Altmetrics Handle Statistics
Altmetrics DOI Statistics
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.
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
Pacific Journal of Mathematics
Copyright © 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.
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.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.