# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.333178

Arkiv for Matematik, 48, (2), 231-242, 2008.8
We give a sufficient condition on a Lévy measure$μ$which ensures that the generator$L$of the corresponding pure jump Lévy process is (locally) hypoelliptic, i.e., $\mathop {\mathrm {sing\,supp}}u\subseteq \mathop {\mathrm {sing\,supp}}Lu$ for all admissible$u$. In particular, we assume that $\mu|_{\mathbb {R}^{d}\setminus \{0\}}\in C^{\infty}(\mathbb {R}^{d}\setminus \{0\})$ . We also show that this condition is necessary provided that $\mathop {\mathrm {supp}}\mu$ is compact.
@inproceedings{helmut2008on,
title={On hypoellipticity of generators of Lévy processes},