Abstract
We prove that if μ is a Radon measure on the Heisenberg group Hn such that the density θ sμ), computed with respect to the Korányi metric dH, exists and is positive and finite on a set of positive μ measure, then s is an integer. The proof relies on an analysis of uniformly distributed measures on Hn, dH. We provide a number of examples of such measures, illustrating both the similarities and the striking differences of this sub-Riemannian setting from its Euclidean counterpart.
Original language | English (US) |
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Pages (from-to) | 771-788 |
Number of pages | 18 |
Journal | Bulletin of the London Mathematical Society |
Volume | 47 |
Issue number | 5 |
DOIs | |
State | Published - Nov 6 2014 |
ASJC Scopus subject areas
- Mathematics(all)