Global heat kernel estimates for symmetric jump processes
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- by Zhen-Qing Chen, Panki Kim and Takashi Kumagai PDF
- Trans. Amer. Math. Soc. 363 (2011), 5021-5055
Corrigendum: Trans. Amer. Math. Soc. 367 (2015), 7515-7515.
Abstract:
In this paper, we study sharp heat kernel estimates for a large class of symmetric jump-type processes in $\mathbb R^d$ for all $t>0$. A prototype of the processes under consideration are symmetric jump processes on $\mathbb R^d$ with jumping intensity \[ \frac {1}{\Phi (|x-y|)} \int _{[\alpha _1, \alpha _2]} \frac {c(\alpha , x,y)} {|x-y|^{d+\alpha }} \nu (d\alpha ) , \] where $\nu$ is a probability measure on $[\alpha _1, \alpha _2] \subset (0, 2)$, $\Phi$ is an increasing function on $[ 0, \infty )$ with $c_1e^{c_2r^{\beta }} \le \Phi (r) \le c_3 e^{c_4r^{\beta }}$ with $\beta \in (0,\infty )$, and $c(\alpha , x, y)$ is a jointly measurable function that is bounded between two positive constants and is symmetric in $(x, y)$. They include, in particular, mixed relativistic symmetric stable processes on $\mathbb {R}^d$ with different masses. We also establish the parabolic Harnack principle.References
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Additional Information
- Zhen-Qing Chen
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- MR Author ID: 242576
- ORCID: 0000-0001-7037-4030
- Email: zchen@math.washington.edu
- Panki Kim
- Affiliation: Department of Mathematical Science, Seoul National University, Seoul 151-747, South Korea
- MR Author ID: 705385
- Email: pkim@snu.ac.kr
- Takashi Kumagai
- Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
- MR Author ID: 338696
- Email: kumagai@kurims.kyoto-u.ac.jp
- Received by editor(s): March 23, 2010
- Published electronically: March 10, 2011
- Additional Notes: The first author’s research was partially supported by NSF Grant DMS-0906743.
The second author’s research was supported by a National Research Foundation of Korea Grant funded by the Korean Government (2009-0087117)
The second and the third authors’ research was partially supported by the Global COE program at the Department of Mathematics, Faculty of Science, Kyoto University. - © Copyright 2011 Zhen-Qing Chen, Panki Kim, and Takashi Kumagai
- Journal: Trans. Amer. Math. Soc. 363 (2011), 5021-5055
- MSC (2010): Primary 60J75, 60J35; Secondary 31C25, 31B05
- DOI: https://doi.org/10.1090/S0002-9947-2011-05408-5
- MathSciNet review: 2806700