☆ 4.3 Article

Heat Kernel Bounds on Metric Measure Spaces and Some Applications

POTENTIAL ANALYSIS (2016)

Journal

POTENTIAL ANALYSIS

Volume 44, Issue 3, Pages 601-627

Publisher

SPRINGER

DOI: 10.1007/s11118-015-9521-2

Keywords

Metric measure space; Ricci curvature; Heat kernel; Heat equation; Riesz transform

Categories

Mathematics

Funding

NSFC [11301029, 11201492]
NSFCs [11401403, 11371099]
ARC [DP130101302]
Guangdong Natural Science Foundation [S2012040007550]

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Abstract

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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