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|),|∇Ptf|⩽KPt(|∇f|), where PtPt 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].