Parabolic Harnack Inequalities and Riesz Transforms on Lie Groups of Polynomial growth

Abstract

Let Gbe a connected Lie group of polynomial growth, i.e. if dgis a left invariant Haar measure and Va compact neighborhood of the identity element eof G, then there are constants c, d> 0 such that dg — measure(V n ) ≤ cn d , n∈ N. Notice that the connected nilpotent Lie groups are of polynomial growth.