Sub-Laplacian with drift in nilpotent Lie groups
Volume 96 / 2003
Colloquium Mathematicum 96 (2003), 41-53
MSC: Primary 22E25, 22E30; Secondary 43A80.
DOI: 10.4064/cm96-1-5
Abstract
We consider the heat kernel $\phi _t$ corresponding to the left invariant sub-Laplacian with drift term in the first commutator of the Lie algebra, on a nilpotent Lie group. We improve the results obtained by G. Alexopoulos in [1], [2] proving the “exact Gaussian factor” $\mathop {\rm exp}\nolimits \left (-{| g| ^2\over 4(1+\varepsilon )t} \right)$ in the large time upper Gaussian estimate for $\phi _t$. We also obtain a large time lower Gaussian estimate for $\phi _t$.
