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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-3-3,
author = {Longjie Xie and Xicheng Zhang},
title = {Heat kernel estimates for critical fractional diffusion operators},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {221-263},
zbl = {1309.47054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-3-3}
}
Longjie Xie; Xicheng Zhang. Heat kernel estimates for critical fractional diffusion operators. Studia Mathematica, Tome 223 (2014) pp. 221-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-3-3/