Harnack inequality and H\" older regularity estimates for a L\' evy process with small jumps of high intensity

Abstract

We consider a L\' evy process in ${\mathbb{R}}^d$ $(d\ge 3)$ with the characteristic exponent \[ Φ(ξ)=\frac{|ξ|^2}{\ln(1+|ξ|^2)}-1. \] The scale invariant Harnack inequality and apriori estimates of harmonic functions in H\" older spaces are proved.

20 pages