Heat kernel bounds for nonlocal operators with singular kernels

Moritz Kassmann*, Kyung Youn Kim, Takashi Kumagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We prove sharp two-sided bounds of the fundamental solution for integro-differential operators of order α∈(0,2) that generate a d-dimensional Markov process. The corresponding Dirichlet form is comparable to that of d independent copies of one-dimensional jump processes, i.e., the jumping measure is singular with respect to the d-dimensional Lebesgue measure.

Original languageEnglish
Pages (from-to)1-26
Number of pages26
JournalJournal des Mathematiques Pures et Appliquees
Publication statusPublished - 2022 Aug
Externally publishedYes


  • Heat kernel
  • Integro-differential operator
  • Markov jump process

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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