Stability of heat kernel estimates for symmetric non-local dirichlet forms

Zhen Qing Chen, Takashi Kumagai, Jian Wang

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for α-stable-like processes even with α ≥ 2 when the underlying spaces have walk dimensions larger than 2, which has been one of the major open problems in this area.

Original languageEnglish
Pages (from-to)1-100
Number of pages100
JournalMemoirs of the American Mathematical Society
Volume271
Issue number1330
DOIs
Publication statusPublished - 2021
Externally publishedYes

Keywords

  • Capacity
  • Cut-off Sobolev inequality
  • Dirichlet form
  • Exit time
  • Faber-Krahn inequality
  • Heat kernel estimate
  • Lévy system,jumping kernel
  • Metric measure space
  • Stability
  • Symmetric jump process

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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