Gradient Estimates for the Subelliptic Heat Kernel on H-type Groups
نویسنده
چکیده
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 H.-Q. Li [10] for the Heisenberg group. The proof is based on pointwise heat kernel estimates, and follows an approach used by Bakry, Baudoin, Bonnefont, and Chafäı [3].
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