Geodesic
Heat kernel estimates for critical fractional diffusion operators
Longjie Xie 1   ; Xicheng Zhang 1
1 School of Mathematics and Statistics Wuhan University Wuhan, Hubei 430072, P.R. China
Studia Mathematica, Tome 224 (2014) no. 3, pp. 221-263 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We construct the heat kernel of the $1/2$-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.
DOI : 10.4064/sm224-3-3
Keywords: construct heat kernel order laplacian perturbed first order gradient term lder spaces zero order potential term generalized kato class obtain sharp two sided estimates gradient estimate heat kernel where proof lower bound based probabilistic approach

Longjie Xie  1   ; Xicheng Zhang  1

1 School of Mathematics and Statistics Wuhan University Wuhan, Hubei 430072, P.R. China 
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Longjie Xie; Xicheng Zhang. Heat kernel estimates for critical fractional diffusion operators. Studia Mathematica, Tome 224 (2014) no. 3, pp. 221-263. doi: 10.4064/sm224-3-3

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