Non-symmetric Lévy-type operators

Abstract

We prove the uniqueness and existence of a weak fundamental solution for the equation ∂ t = L for non-symmetric non-local operatorsunder certain assumptions on b, κ and J. The result allows us to cover new coefficients even for the 1-stable Lévy measure J(z) = |z| −d−1 . We formalize and then use a general abstract approach to the parametrix construction.