On $$L^{p}$$ L p -theory for parabolic and elliptic integro-differential equations with scalable operators in the whole space

Abstract

Elliptic and parabolic integro-differential model problems are considered in the whole space. By verifying Hormander condition, the existence and uniqueness is proved in \(L_{p}\)-spaces of functions whose regularity is defined by a scalable, possibly nonsymmetric, Levy measure. Some rough probability density function estimates of the associated Levy process are used as well.