Centered sub-Laplacians and densities in Lie groups of polynomial volume growth
AuthorAlexopoulos, Georgios K.
SourceComptes Rendus de l'Academie des Sciences - Series I: Mathematics
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We prove a Harnack inequality on connected Lie groups of polynomial volume growth. We use this inequality to study the large time behavior of the heat kernels associated to centered sub-Laplacians. Thus, we obtain Gaussian estimates and estimates of the type Berry - Esseen. We also obtain similar results for the convolution powers of centered densities. © 1998 Académie des Sciences/Elsevier, Paris.