On the equivalence of parabolic Harnack inequalities and heat kernel estimates

Martin T. Barow*, Alexander Grigor'yan, Takashi Kumagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)

Abstract

We prove the equivalence of parabolic Harnack inequalities and sub-Gaussian heat kernel estimates in a general metric measure space with a local regular Dirichlet form.

Original languageEnglish
Pages (from-to)1091-1146
Number of pages56
JournalJournal of the Mathematical Society of Japan
Volume64
Issue number4
DOIs
Publication statusPublished - 2012
Externally publishedYes

Keywords

  • Caloric function
  • Dirichlet space
  • Harnack inequality
  • Heat kernel estimate
  • Metric measure space
  • Volume doubling

ASJC Scopus subject areas

  • Mathematics(all)

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