On the Solvability of Riemann–Hilbert Problem in the Weighted Smirnov Classes

Abstract

In this paper the Riemann–Hilbert problem of the theory of analytic functions in weighted Smirnov classes is considered. Under certain conditions on the coefficients, the Noetherness of this problem is proved. In the case of solvability general solutions of homogeneous and also non-homogeneous Riemann–Hilbert problem are constructed. As sufficient condition on the weight function for the solvability of the corresponding problems is obtained.