Gradient Estimates for the Subelliptic Heat Kernel on H-type Groups

Details Gradient Estimates for the Subelliptic Heat Kernel on H-type Groups Gradient Estimates for the Subelliptic Heat Kernel on H-type Groups

2009-04-11

arxiv.org/abs/0904.1781v1

Mathematics

Analysis of PDEs

Submitted to J. Funct. Anal

Scientific paper

We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups $G$ of H-type: \abs{\grad P_t f} \le K P_t(\abs{\grad f}) where $P_t$ is the heat semigroup corresponding to the sublaplacian on $G$, $\grad$ 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 Chafa\"i.

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