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

Abstract

We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups $G$ of H-type: $$|\nabla P_{t}f|\le K{P}_t(|\nabla f|)$$ where $P_t$ is the heat semigroup corresponding to the sublaplacian on $G$, $\nabla$ is the subelliptic gradient, and $K$ is a constant. This extends a result of H.-Q. Li for the Heisenberg group. The proof is based on pointwise heat kernel estimates, and follows an approach used by Bakry, Baudoin, Bonnefont, and Chafaï.

23 pages; updated with peer-review revisions

References in corpus (2)

• On gradient bounds for the heat kernel on the Heisenberg group
• Precise estimates for the subelliptic heat kernel on H-type groups

Cited by in corpus (4)

• On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group
• Strong hypercontractivity and strong logarithmic Sobolev inequalities for log-subharmonic functions on stratified Lie groups
• Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups
• On gradient estimates of the heat semigroups on step-two Carnot groups