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Stability of heat kernel estimates and parabolic Harnack inequalities for general symmetric pure jump processes
| Content Provider | Scilit |
|---|---|
| Author | Chen, Zhen-Qing Kumagai, Takashi Wang, Jian |
| Copyright Year | 2021 |
| Abstract | In this paper, we survey recent work on heat kernel estimates for general symmetric pure jump processes on a metric measure space (M, ρ, μ) generated by the following type of nonlocal Dirichlet forms: ℰ(f , g) = ∫ M×M (f (x) − f (y))(g(x) − g(y))J(dx, dy), where J(dx, dy) is a symmetric Radon measure on M × M \ diag that may have different growth behaviors for small and large jumps. Under general volume doubling condition on (M, ρ, μ) and some mild quantitative assumptions on J(dx, dy) that are allowed to have light tails of polynomial decay at infinity, we present stability results for two-sided heat kernel estimates and heat kernel upper bounds, as well as the corresponding parabolic Harnack inequalities. The results extend considerably those for mixture of symmetric stable-like jump processes in metric measure spaces, and more interestingly, they have connections to these for symmetric diffusions with jumps. |
| Related Links | https://www.degruyter.com/downloadpdf/book/9783110700763/10.1515/9783110700763-001.pdf |
| DOI | 10.1515/9783110700763-001 |
| Language | English |
| Publisher | Walter de Gruyter GmbH |
| Publisher Date | 2021-01-18 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Heat Kernel Estimates Symmetric Behaviors Jump Processes Measure Spaces |
| Content Type | Text |
| Resource Type | Chapter |
