Asymptotics of solutions of the linear conjugation problem at the corner points of the curve

Abstract

We consider the classical linear conjugation problem for analytic functions on a piecewise smooth curve in the entire scale of weighted Hölder spaces. We derive a closed-form power-logarithmic asymptotics of the solution of this problem at the corner points of the curve under the assumption that the right-hand side of the problem admits a similar asymptotics.