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Sub-Laplacian with drift in nilpotent Lie groups

Camillo Melzi — 2003

Colloquium Mathematicae

We consider the heat kernel $ϕ_{t}$ 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” exp(-|g|²/4(1+ε)t) in the large time upper Gaussian estimate for $ϕ_{t}$ . We also obtain a large time lower Gaussian estimate for $ϕ_{t}$ .

Large time estimates for non-symmetric heat kernel on the affine group

Camillo Melzi — 2002

Annales mathématiques Blaise Pascal

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