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Heat kernel estimates for critical fractional diffusion operators

Tom 224 / 2014

Longjie Xie, Xicheng Zhang Studia Mathematica 224 (2014), 221-263 MSC: Primary 60J35; Secondary 47G20. DOI: 10.4064/sm224-3-3

Streszczenie

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.

Autorzy

  • Longjie XieSchool of Mathematics and Statistics
    Wuhan University
    Wuhan, Hubei 430072, P.R. China
    e-mail
  • Xicheng ZhangSchool of Mathematics and Statistics
    Wuhan University
    Wuhan, Hubei 430072, P.R. China
    e-mail

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