Heat kernel estimates for critical fractional diffusion operators
Volume 224 / 2014
Studia Mathematica 224 (2014), 221-263 MSC: Primary 60J35; Secondary 47G20. DOI: 10.4064/sm224-3-3
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.