几何分析系列报告之03【胡二彦】

报告摘要：Let d ≥ 2, α ∈ (0,2), and X be the cylindrical α-stable process on R^d. We first present a geometric characterization of open subset D ⊂R^d so that the part process X^D of X in D is irreducible. We then study the properties of the transition density functions of X^D, including the strict positivity property as well as their sharp two-sided bounds in C^1,1 domains in R^d. Our bounds are shown to be sharp for a class of C^1,1 domains.