The Szegö function on a non-rectifiable arc

Let Γ be a simple Jordan arc in the complex plane. The Szegö function, by definition, is a holomorphic in ? \ Γ function with a prescribed product of its boundary values on Γ. The problem of finding the Segö function in the case of piecewise smooth Γ was solved earlier. In this paper we study this problem for non-rectifiable arcs. The solution relies on properties of the Cauchy transform of certain distributions with the support on Γ.