Potential spaces and traces of Lévy processes on h-sets

Abstract

Potential spaces and Dirichlet forms associated with Levy processes subordinate to Brownian motion in ℝn with generator f(−Δ) are investigated. Estimates for the related Rieszand Bessel-type kernels of order s are derived which include the classical case f(r) = rα/2 with 0 < α < 2 corresponding to α-stable Levy processes. For general (tame) Bernstein functions f potential representations of the trace spaces, the trace Dirichlet forms, and the trace processes on fractal h-sets are derived. Here we suppose the trace condition ∫01r−(n+1)f(r−2)−1h(r) dr < ∞ on f and the gauge function h.