Zoran Vondraček

Let \(Z\) be an isotropic stable process in the Euclidean space. The process \(Z\) is killed upon exiting an open set \(D\) and the killed process is then subordinated by an independent \(\gamma\)-stable subordinator, \(0<\gamma <1\). The resulting process is a Hunt process in \(D\). In this talk, I will discuss several potential theoretical properties of this process such as Harnack inequality for nonnegative harmonic functions, the Carleson estimate, Green function and jumping kernel estimates in smooth sets \(D\), and in particular, the boundary Harnack principle. Surprisingly, it turns out the BHP holds only if \(1/2<\gamma<1\). This is joint work with Panki Kim and Renming Song.