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

We consider a L\' evy process in $\R^d$ $(d\geq 3)$ 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.

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