$C^{1+\alpha }$ regularity for fractional $p$-harmonic functions

We establish interior $C^{1,\alpha }$ regularity estimates for some $\alpha >0$, for solutions of the fractional $p$-Laplace equation $(-{\mathrm{\Delta }}_p{)}^{s}u=0$ when $p$ is in the range $p\in [2,2\mathrm{/}(1-s))$.