Abstract
In this paper we study potential-theoretic properties of the symmetric α-stable processes (0<α<2): establishing the boundary Harnack principle for ratios of α-harmonic functions on any open sets, identifying the Martin boundary with the Euclidean boundary for open sets with a certain interior fatness property, and extending earlier results on intrinsic ultracontractivity and the conditional gauge theorem to certain open sets.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 403-427 |
| Number of pages | 25 |
| Journal | Journal of Functional Analysis |
| Volume | 168 |
| Issue number | 2 |
| DOIs | |
| State | Published - Nov 10 1999 |
Keywords
- Boundary Harnack principle
- Conditional gauge theorem
- Intrinsic ultracontractivity
- Martin boundary
- Symmetric stable processes
ASJC Scopus subject areas
- Analysis