Heat Kernel Bounds on Metric Measure Spaces and Some Applications
Heat Kernel Bounds on Metric Measure Spaces and Some Applications
复制标题
度量测度空间上的热核界限及一些应用
DOI：
10.1007/s11118-015-9521-2
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发表时间：
2016
影响因子：
1.1
通讯作者：
Zhang Huichun
中科院分区：
文献类型：
--
作者：
Jiang Renjin;Li Huaiqian;Zhang Huichun
设（X，d，μ）是RCD空间，且N ∈[1，∞）.利用抛物Harnack不等式和比较原理，得到了（X，d，μ）上热核的上、下界及其梯度的精确界，该界在时间上也是精确的.作为应用，我们研究了热核的大时间行为，热方程解的稳定性，并证明了（局部）Riesz变换的Lp有界性。
Let (X,d,μ) be aRCD∗(K,N) space withandN∈[1,∞). We derive the upper and lower bounds of the heat kernel on (X,d,μ) by applying the parabolic Harnack inequality and the comparison principle, and then sharp bounds for its gradient, which are also sharp in time. For applications, we study the large time behavior of the heat kernel, the stability of solutions to the heat equation, and show theLpboundedness of (local) Riesz transforms.