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arXiv · 0904.1781

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

Nathaniel Eldredge
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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.

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Nathaniel Eldredge. 2014-06-24. Gradient estimates for the subelliptic heat kernel on H-type groups. https://doi.org/10.1016/j.jfa.2009.08.012

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