Inserted: 23 apr 2003
Last Updated: 27 apr 2004
Journal: Journal of Functional Analysis
For a general Carnot group $G$ with homogenous dimension $Q$ we prove the existence of a fundamental solution of the $Q$-Laplacian whose exponential is a homogenous norm on $G$. This implies a sharp version of the celebrated Moser-Trudinger inequality.
Keywords: Carnot group, Q-Laplacian , Fundamental solution, Moser-Trudinger inequality