Bellman-Krein formula for an integral equation with kernel of the type k(x,y)=k(x - y) x- y sup(-α)

With the aid of the Bellman-Krein formula for the resolvent, it is shown how to solve the integral equation with kernel of the type k(x,y)=k(x - y) x - ysup(-α), 0<α<n, i.e. the kernel with weak singularity