Estimates of gradient of $\mathcal{L}$-harmonic functions for nonlocal operators with order $\alpha >1$

Tomasz Grzywny, Tomasz Jakubowski, Grzegorz Żurek

We obtain Grönwall type estimates for the gradient of the harmonic functions for a Lévy operator with order strictly larger than 1 and minimal assumptions of its Lévy measure.