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Gradient Estimates for the Subelliptic Heat Kernel on Htype Groups
, 2009
"... We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups G of Htype: ∇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 ..."
Abstract

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We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups G of Htype: ∇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 Chafaï [3].
DOI 10.1007/s0003001202159 Nonlinear Differential Equations
"... Large time behavior for the heat equation on Carnot groups ..."
HYPOELLIPTIC HEAT KERNELS ON INFINITEDIMENSIONAL HEISENBERG GROUPS
"... Abstract. We study the law of a hypoelliptic Brownian motion on an infinitedimensional Heisenberg group based on an abstract Wiener space. We show that the endpoint distribution, which can be seen as a heat kernel measure, is absolutely continuous with respect to a certain product of Gaussian and L ..."
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Abstract. We study the law of a hypoelliptic Brownian motion on an infinitedimensional Heisenberg group based on an abstract Wiener space. We show that the endpoint distribution, which can be seen as a heat kernel measure, is absolutely continuous with respect to a certain product of Gaussian and Lebesgue measures, that the heat kernel is quasiinvariant under translation by the Cameron–Martin subgroup, and that the Radon–Nikodym derivative is Malliavin smooth. Contents