NASH-TYPE INEQUALITIES AND HEAT KERNELS FOR NON-LOCAL DIRICHLET FORMS

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概要

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• We use an elementary method to obtain Nash-type inequalities for nonlocal 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. Stochastic Process Appl. $ \mathbf{108} $(2003), 27-62).

• Faculty of Mathematics, Kyushu Universityの論文

著者

• Kumagai Takashi

  Research Institute For Mathematical Sciences Kyoto University

• HU Jiaxin

  Department of Mathematical Sciences Tsinghua University

関連論文

• Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms
• Stability of parabolic Harnack inequalities on metric measure spaces
• NASH-TYPE INEQUALITIES AND HEAT KERNELS FOR NON-LOCAL DIRICHLET FORMS

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