Extension of CR functions into wedges through families of non-smooth analytic discs

The goal of this paper is to develop a theory of nonsmooth analytic discs attached to domains with Lipschitz boundary in real submanifolds of Cn. We then apply this technique to establish a propagation principle for wedge extendibility of CR-functions on these domains along CR-curves and along boundaries of attached analytic discs. The technique from this paper has been also extensively used by the authors recently to obtain sharp results on wedge extension of CR-functions on wedges in prescribed directions extending results of Boggess-Polking and Eastwood-Graham.