Heat kernel estimates for jump processes of mixed types on metric measure spaces
 ZhenQing Chen,
 Takashi Kumagai
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In this paper, we investigate symmetric jumptype processes on a class of metric measure spaces with jumping intensities comparable to radially symmetric functions on the spaces. The class of metric measure spaces includes the Alfors dregular sets, which is a class of fractal sets that contains geometrically selfsimilar sets. A typical example of our jumptype processes is the symmetric jump process with jumping intensity \(e^{c_0 (x, y)xy}\, \int_{\alpha_1}^{\alpha_2} \frac{c(\alpha, x, y)}{xy^{d+\alpha}} \, \nu (d\alpha)\) where ν is a probability measure on \([\alpha_1, \alpha_2]\subset (0, 2)\) , c(α, x, y) is a jointly measurable function that is symmetric in (x, y) and is bounded between two positive constants, and c _{0}(x, y) is a jointly measurable function that is symmetric in (x, y) and is bounded between γ_{1} and γ_{2}, where either γ_{2} ≥ γ_{1} > 0 or γ_{1} = γ_{2} = 0. This example contains mixed symmetric stable processes on \({\mathbb{R}}^n\) as well as mixed relativistic symmetric stable processes on \({\mathbb{R}}^n\) . We establish parabolic Harnack principle and derive sharp twosided heat kernel estimate for such jumptype processes.
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 Title
 Heat kernel estimates for jump processes of mixed types on metric measure spaces
 Journal

Probability Theory and Related Fields
Volume 140, Issue 12 , pp 277317
 Cover Date
 20080101
 DOI
 10.1007/s0044000700705
 Print ISSN
 01788051
 Online ISSN
 14322064
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Primary: 60J75
 60J35
 Secondary: 31C25
 31C05
 Industry Sectors
 Authors

 ZhenQing Chen ^{(1)}
 Takashi Kumagai ^{(2)}
 Author Affiliations

 1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA
 2. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 6068502, Japan