Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms

Zhen Qing Chen, Takashi Kumagai, Jian Wang*

*この研究の対応する著者

研究成果: Article査読

3 被引用数 (Scopus)

抄録

In this paper, we consider the following symmetric Dirichlet forms on a metric measure space (M,d,μ): E(f,g)=E(c)(f,g)+∫M×M(f(x)−f(y))(g(x)−g(y))J(dx,dy), where E(c) is a strongly local symmetric bilinear form and J(dx,dy) is a symmetric Radon measure on M×M. Under general volume doubling condition on (M,d,μ) and some mild assumptions on scaling functions, we establish stability results for upper bounds of heat kernel (resp. two-sided heat kernel estimates) in terms of the jumping kernels, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp. the Poincaré inequalities). We also obtain characterizations of parabolic Harnack inequalities. Our results apply to symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than 2.

本文言語English
論文番号107269
ジャーナルAdvances in Mathematics
374
DOI
出版ステータスPublished - 2020 11月 18
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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