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Optimal gradient estimates of heat kernels of stable-like operators


Authors: Kai Du and Xicheng Zhang
Journal: Proc. Amer. Math. Soc. 147 (2019), 3559-3565
MSC (2010): Primary 60G52, 35K08
DOI: https://doi.org/10.1090/proc/14489
Published electronically: April 3, 2019
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Abstract: In this note we show the optimal gradient estimate for heat kernels of stable-like operators by providing a counterexample.


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Additional Information

Kai Du
Affiliation: Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
Email: kdu@fudan.edu.cn

Xicheng Zhang
Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, People’s Republic of China
Email: XichengZhang@gmail.com

DOI: https://doi.org/10.1090/proc/14489
Keywords: Gradient estimate, heat kernel, stable-like operators
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
Article copyright: © Copyright 2019 American Mathematical Society