## Monday Analysis Seminar: Heat kernel estimates and parabolic Harnack inequalities for jump processes on metric measure spaces

Date
2015-9-28 13:30 - 2015-9-28 14:30
Place
Faculty of Science Buliding #3 Room 210
Speaker/Organizer
Takashi Kumagai (Kyoto University)

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).

Different time. Ancona talks after this lecture.