The Szegö function on a non-rectifiable arc

Let $\Gamma$ be a simple Jordan arc in the complex plane. The Szegö function, by definition, is a holomorphic in $\mathbb C\setminus\Gamma$ function with a prescribed product of its boundary values on $\Gamma$. The problem of finding the Szegö function in the case of piecewise smooth $\Gamma$ 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 $\Gamma$.