Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups
Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups
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重新审视各向同性和非各向同性海森堡群的热核
DOI：
10.1080/03605302.2019.1581802
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发表时间：
2019
影响因子：
1.9
通讯作者：
Zhang Ye
中科院分区：
文献类型：
--
作者：
Li Hong Quan;Zhang Ye
本文的目的有三个方面。首先，我们利用三维情形下的著名结果，得到了各向同性海森堡群热核的精确界。其次，我们研究了各向异性海森堡群上热核在无穷远点的渐近估计。作为结果，我们给出了热核的一致上、下估计，并完善了Beals-Gaveau-Greiner得到的热核的短时行为。第三，我们证明了第一作者所得到的Grushin算子的热核在无穷远处的一致渐近行为（即小时间渐近行为）在二维和三维中仍然有效。
The aim of this paper is threefold. First, we obtain the precise bounds for the heat kernel on isotropic Heisenberg groups by using well-known results in the three-dimensional case. Second, we study the asymptotic estimates at infinity for the heat kernel on nonisotropic Heisenberg groups. As a consequence, we give uniform upper and lower estimates of the heat kernel, and complete its short-time behavior obtained by Beals–Gaveau–Greiner. Third, we prove that the uniform asymptotic behaviour at infinity (so the small-time asymptotic behaviour) of the heat kernel for Grushin operators, obtained by the first author, are still valid in two and three dimensions.