Potential theory of subordinate Brownian motions

Renming Song

Abstract:
A subordinate Brownian motion can be obtained by replacing the time
parameter of a Brownian motion by an increasing Levy process (i.e.,
subordinator). Subordinate Brownian motions are very important in
various applications. In this talk, I will give a survey of some recent
results in the study of subordinate Brownian motions. In particular, I
will present sharp two-sided estimates on the Green functions and heat 
kernels of subordinate Brownian motions in bounded smooth open sets.