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Regularity Versus Smoothness of Measures by Fraser, Jonathan M.; Troscheit, Sascha is a scholarly article available to read on EtoBox.

What is Regularity Versus Smoothness of Measures about?

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 $L^p$ 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.

Author

Fraser, Jonathan M.; Troscheit, Sascha

Published

2019

Language

EN