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

Jiaxin Hu; Takashi Kumagai

doi:10.2206/kyushujm.60.245

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

Jiaxin Hu^*, Takashi Kumagai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	245-265
Number of pages	21
Journal	Kyushu Journal of Mathematics
Volume	60
Issue number	2
DOIs	https://doi.org/10.2206/kyushujm.60.245
Publication status	Published - 2007 May 10
Externally published	Yes

Keywords

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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10.2206/kyushujm.60.245

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AB - 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.

KW - Dirichlet forms

KW - Fractals

KW - Heat kernels

KW - Jump processes

KW - Lévy system

KW - Nash's inequality

KW - Parabolic Harnack inequality

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JO - Kyushu Journal of Mathematics

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

Abstract

Keywords

ASJC Scopus subject areas

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