Strong existence and uniqueness for stable stochastic differential equations with distributional drift

We consider the stochastic differential equation dXt=b(Xt)dt+dLt, where the drift b is a generalized function and L is a symmetric one dimensional .-stable Lévy processes, ..(1,2). We define the notion of solution to this equation and establish strong existence and uniqueness whenever b belongs to the Besov.Hölder space C. for .>1/2../2.