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Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

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Abstract

In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation

$${{\cal S}^b}: = {\overline {\rm{\Delta }} ^{\alpha /2}} + b \cdot \nabla $$

where \({\overline {\rm{\Delta }} ^{\alpha /2}}\) is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ K α−1d . In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.

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Acknowledgements

The author is grateful to Professor Zhen-Qing Chen for valuable comments on an earlier version of this paper.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, P. R. China

    Jie Ming Wang

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  1. Jie Ming Wang
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Correspondence to Jie Ming Wang.

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Partially supported by NSFC (Grant Nos. 11731009 and 11401025)

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Wang, J.M. Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes. Acta. Math. Sin.-English Ser. 37, 229–248 (2021). https://doi.org/10.1007/s10114-020-9459-1

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