Heat kernel upper bounds for jump processes and the first exit time
Heat kernel upper bounds for jump processes and the first exit time
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DOI：
10.1515/crelle.2009.005
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Barlow;A. Grigor’yan;T. Kumagai
中科院分区：
文献类型：
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作者：
M. Barlow;A. Grigor’yan;T. Kumagai
对于所有t> 0，x∈M和f∈L2（m，μ）。与r n中的热半群{
for all t > 0, x ∈ M , and f ∈ L2(M,μ). The function pt(x, y) can be considered as the transition density of the associated Markov processX = {Xt}t≥0, and the question of estimating of pt(x, y), which is the main subject of this paper, is closely related to the properties of X. The function pt(x, y) is also referred to as a heat kernel, and this terminology goes back to the classical Gauss-Weierstrass heat kernel associated with the heat semigroup {e}t≥0 in R n, whose Markov process is Brownian motion. A somewhat more general but still well treated case is when (M,d, μ) is a Riemannian metric measure space, that is, M is a Riemannian manifold,