Optimal gradient estimates of heat kernels of stable-like operators
HTML articles powered by AMS MathViewer
- by Kai Du and Xicheng Zhang PDF
- Proc. Amer. Math. Soc. 147 (2019), 3559-3565 Request permission
Abstract:
In this note we show the optimal gradient estimate for heat kernels of stable-like operators by providing a counterexample.References
- Krzysztof Bogdan and Tomasz Jakubowski, Estimates of heat kernel of fractional Laplacian perturbed by gradient operators, Comm. Math. Phys. 271 (2007), no. 1, 179–198. MR 2283957, DOI 10.1007/s00220-006-0178-y
- Zhen-Qing Chen and Takashi Kumagai, Heat kernel estimates for jump processes of mixed types on metric measure spaces, Probab. Theory Related Fields 140 (2008), no. 1-2, 277–317. MR 2357678, DOI 10.1007/s00440-007-0070-5
- Zhen-Qing Chen and Xicheng Zhang, Heat kernels and analyticity of non-symmetric jump diffusion semigroups, Probab. Theory Related Fields 165 (2016), no. 1-2, 267–312. MR 3500272, DOI 10.1007/s00440-015-0631-y
- Zhen-Qing Chen and Xicheng Zhang, Heat kernels for time-dependent non-symmetric stable-like operators, J. Math. Anal. Appl. 465 (2018), no. 1, 1–21. MR 3806688, DOI 10.1016/j.jmaa.2018.03.054
- P. Jin, Heat kernel estimates for non-symmetric stable-like processes, https://arxiv.org/abs/ 1709.02836.
- Victoria Knopova and Alexei Kulik, Parametrix construction of the transition probability density of the solution to an SDE driven by $\alpha$-stable noise, Ann. Inst. Henri Poincaré Probab. Stat. 54 (2018), no. 1, 100–140 (English, with English and French summaries). MR 3765882, DOI 10.1214/16-AIHP796
- Tadeusz Kulczycki and MichałRyznar, Gradient estimates of harmonic functions and transition densities for Lévy processes, Trans. Amer. Math. Soc. 368 (2016), no. 1, 281–318. MR 3413864, DOI 10.1090/tran/6333
- Tadeusz Kulczycki and MichałRyznar, Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes, Math. Nachr. 291 (2018), no. 2-3, 374–397. MR 3767143, DOI 10.1002/mana.201600443
Additional Information
- Kai Du
- Affiliation: Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
- MR Author ID: 918246
- Email: kdu@fudan.edu.cn
- Xicheng Zhang
- Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, People’s Republic of China
- MR Author ID: 652168
- Email: XichengZhang@gmail.com
- Received by editor(s): August 11, 2018
- Received by editor(s) in revised form: October 29, 2018
- Published electronically: April 3, 2019
- Additional Notes: Research of the first author was partially supported by NSF grant of China (No. 11801084).
Research of the second author was partially supported by NNSFC grant of China (No. 11731009) and the DFG through the CRC 1283 “Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications”. - Communicated by: Zhen-Qing-Chen
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3559-3565
- MSC (2010): Primary 60G52, 35K08
- DOI: https://doi.org/10.1090/proc/14489
- MathSciNet review: 3981133