Gevrey regularity for integro-differential operators

We prove for some singular kernels K(x,y) that viscosity solutions of the integro-differential equation∫Rn[u(x+y)+u(x−y)−2u(x)]K(x,y)dy=f(x) locally belong to some Gevrey class if so does f. The fractional Laplacian equation is included in this framework as a special case.