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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.
Longjie Xie, and Xicheng Zhang. "Heat kernel estimates for critical fractional diffusion operators." Studia Mathematica 224.3 (2014): 221-263. <http://eudml.org/doc/285751>.
@article{LongjieXie2014, abstract = {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.}, author = {Longjie Xie, Xicheng Zhang}, journal = {Studia Mathematica}, keywords = {heat kernel estimate; gradient estimate; critical diffusion operator; Levi's method}, language = {eng}, number = {3}, pages = {221-263}, title = {Heat kernel estimates for critical fractional diffusion operators}, url = {http://eudml.org/doc/285751}, volume = {224}, year = {2014}, }
TY - JOUR AU - Longjie Xie AU - Xicheng Zhang TI - Heat kernel estimates for critical fractional diffusion operators JO - Studia Mathematica PY - 2014 VL - 224 IS - 3 SP - 221 EP - 263 AB - 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. LA - eng KW - heat kernel estimate; gradient estimate; critical diffusion operator; Levi's method UR - http://eudml.org/doc/285751 ER -