月曜解析セミナー： 測度付き距離空間の上の飛躍型確率過程の熱核評価、ハルナック不等式について

2015年 　 9月 28日 13時 30分 ～ 2015年 　 9月 28日 14時 30分

We consider mixed-type jump processes on metric measure spaces and discuss the stability of two-sided heat kernel estimates and parabolic Harnack inequalities. Under the assumption of volume doubling, we establish their equivalent characterizations in terms of the jump kernels and the Poincar\'e inequalities. These are non-local versions of the cerebrated work by Grigor'yan and Saloff-Coste concerning the stability of parabolic Harnack inequalities. We note that for $\alpha$-stable-like processes, our current results are restricted to $\alpha < 2$.
This is a on-going joint work with Z.Q. Chen (Seattle) and J. Wang (Fuzhou and Kyoto).