Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings

Soobin Cho, Panki Kim, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we discuss non-local operators with killing potentials, which may not be in the standard Kato class. We first discuss factorization of their Dirichlet heat kernels in metric measure spaces. Then we establish explicit estimates of the Dirichlet heat kernels under critical killings in C1,1 open subsets of Rd or in Rd∖{0}. The decay rates of our explicit estimates come from the values of the multiplicative constants in the killing potentials. Our method also provides an alternative and unified proof of the main results of [18–20].

Original languageEnglish (US)
Pages (from-to)208-256
Number of pages49
JournalJournal des Mathematiques Pures et Appliquees
Volume143
DOIs
StatePublished - Nov 2020

Keywords

  • Critical killings
  • Dirichlet heat kernel
  • Potential
  • Transition density

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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