@article{3af41f68f3894970bb566c7fc0bf20a7,
title = "Heat kernel estimates for critical fractional diffusion operators",
abstract = "We construct the heat kernel of the 1=2-order Laplacian perturbed by a first-order gradient term in H{\"o}lder 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.",
keywords = "Critical diffusion operator, Gradient estimate, Heat kernel estimate, Levi's method",
author = "Longjie Xie and Xicheng Zhang",
note = "Publisher Copyright: {\textcopyright} Instytut Matematyczny PAN, 2014.",
year = "2014",
doi = "10.4064/sm224-3-3",
language = "English",
volume = "224",
pages = "221--263",
journal = "Studia Mathematica",
issn = "0039-3223",
publisher = "Instytut Matematyczny",
number = "3",
}