Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (5): 1240-1248.doi: 10.1007/s10473-020-0506-x

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THE DAVIES METHOD FOR HEAT KERNEL UPPER BOUNDS OF NON-LOCAL DIRICHLET FORMS ON ULTRA-METRIC SPACES

Jin GAO   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
  • Received:2019-03-12 Revised:2019-09-14 Online:2020-10-25 Published:2020-11-04
  • Supported by:
    The author was supported by National Natural Science Foundation of China (11871296).

Abstract: We apply the Davies method to give a quick proof for the upper estimate of the heat kernel for the non-local Dirichlet form on the ultra-metric space. The key observation is that the heat kernel of the truncated Dirichlet form vanishes when two spatial points are separated by any ball of a radius larger than the truncated range. This new phenomenon arises from the ultra-metric property of the space.

Key words: heat kernel, ultra-metric, Davies method

CLC Number: 

  • 35K08
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