Remarks about the Besicovitch Covering Property in Carnot groups of step 3 and higher

Abstract

We prove that the Besicovitch Covering Property (BCP) does not hold for some classes of homogeneous quasi-distances on Carnot groups of step 3 and higher. As a special case we get that, in Carnot groups of step 3 and higher, BCP is not satisfied for those homogeneous distances whose unit ball centered at the origin coincides with a Euclidean ball centered at the origin. This result comes in contrast with the case of the Heisenberg groups where such distances satisfy BCP.

Locations

• Proceedings of the American Mathematical Society - View
• arXiv (Cornell University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View
• CINECA IRIS Institutial research information system (University of Pisa) - View - PDF