Journal
POTENTIAL ANALYSIS
Volume 44, Issue 3, Pages 601-627Publisher
SPRINGER
DOI: 10.1007/s11118-015-9521-2
Keywords
Metric measure space; Ricci curvature; Heat kernel; Heat equation; Riesz transform
Categories
Funding
- NSFC [11301029, 11201492]
- NSFCs [11401403, 11371099]
- ARC [DP130101302]
- Guangdong Natural Science Foundation [S2012040007550]
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Let (X,d,mu) be a R C D (au)(K,N) space with and Na[1,a). We derive the upper and lower bounds of the heat kernel on (X,d,mu) 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 the L (p) boundedness of (local) Riesz transforms.
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