Riemann–Hilbert problem in a family of weighted Hölder spaces

Resumo

We consider the classical Riemann–Hilbert problem in a simply connected domain bounded by a piecewise smooth contour in the entire scale of weighted H¨older spaces. By using an appropriate refinement of the Kellogg theorem on a conformal mapping of this domain onto a disk, we provide a complete description of the solvability situation for this problem.