Integration over non-rectifiable curves and Riemann boundary value problems (Q534736)

The authors introduce an alternative way of defining the curvilinear Cauchy integral over non-rectifiable curves in the case of complex functions of one complex variable. As an application, solvability conditions for the Riemann boundary value problem are derived under very weak conditions on the boundary. Under some natural assumptions, it is proved that the picture of solvability of this problem coincides with the classical case. The case of complex-valued functions is extended to the case of functions with values in Douglis algebras.