Precise estimates for the subelliptic heat kernel on H-type groups
نویسندگان
چکیده
منابع مشابه
Precise Estimates for the Subelliptic Heat Kernel on H-type Groups
We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups G of H-type. Specifically, we show that there exist positive constants C1, C2 and a polynomial correction function Qt on G such that C1Qte − d2 4t ≤ pt ≤ C2Qte d2 4t where pt is the heat kernel, and d the Carnot-Carathéodory distance on G. We also obtain similar bounds on the norm of its subellip...
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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 approa...
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2009
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2009.04.011