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- Publisher
- Birkhäuser Basel
- Copyright
- © Birkhäuser Basel 2009
- ISBN
- 978-3-0346-0029-3
- Pages
- 3 –44
- DOI
- 10.1007/978-3-0346-0030-9_1
- Publisher site
- See Chapter on Publisher Site
Abstract
[In this survey we discuss heat kernel estimates of self-similar type on metric spaces with doubling measures. We characterize the tail functions from heat kernel estimates in both non-local and local cases. In the local case we also specify the domain of the energy form as a certain Besov space, and identify the walk dimension in terms of the critical Besov exponent. The techniques used include self-improvement of heat kernel upper bound and the maximum principle for weak solutions. All proofs are completely analytic.]
Published: Dec 30, 2009
Keywords: Primary: 47D07; Secondary: 28A80; 46E35; Doubling measure; heat kernel; maximum principle; heat equation