Gradient estimates for the subelliptic heat kernel on H-type groups

We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups G of H-type: |∇Ptf | KPt |∇f | , where Pt is the heat semigroup corresponding to the sublaplacian on G, ∇ is the subelliptic gradient, and K is a constant. This extends a result of Li (2006) [10] for the Heisenberg group. The proof is based on pointwise heat kernel estimates, and follows an approach used by Bakry et al. (2008) [3]. © 2009 Elsevier Inc. All rights reserved.