Potential type operators on curves with vorticity points

We study potential type operators on certain non-Lipschitz curves Γ. The curves under consideration are locally Lyapunov except for a finite set F of singular points. The normal vector ν(y) to the curve F does not have a limit at the singular points and, moreover, ν(y) may be an oscillating and rotating vector function in a neighborhood of the singular points. We establish a Fredholm theory of potential type operators in the spaces L_p,w(Γ, ℂⁿ) where p ∈ (1, ∞) and w is a weight satisfying the Muckenhoupt condition.