Nash-type inequalities and heat kernels for non-local Dirichlet forms

Jiaxin Hu*, Takashi Kumagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


We use an elementary method to obtain Nash-type inequalities for non-local Dirichlet forms on d-sets. We obtain two-sided estimates for the corresponding heat kernels if the walk dimensions of heat kernels are less than two; these estimates are obtained by combining probabilistic and analytic methods. Our arguments partly simplify those used in Chen and Kumagi (Heat kernel estimates for stable-like processes on d-sets.

Original languageEnglish
Pages (from-to)245-265
Number of pages21
JournalKyushu Journal of Mathematics
Issue number2
Publication statusPublished - 2007 May 10
Externally publishedYes


  • Dirichlet forms
  • Fractals
  • Heat kernels
  • Jump processes
  • Lévy system
  • Nash's inequality
  • Parabolic Harnack inequality

ASJC Scopus subject areas

  • Mathematics(all)


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