Riemann boundary value problems in generalized weighted hardy spaces

Abstract

Riemann boundary value problem of analytic function theory in weighted Hardy classes with variable summability index is considered in this work. The Fredholmness of this problem is investigated under certain conditions on coefficients and a weight. The general solution for homogeneous problem is obtained in weighted Hardy classes with variable summability index. In the case where the weight function satisfies the Muckenhoupt condition with variable summability index, the solvability of the non-homogeneous Riemann problem with the right side from the generalized weighted Lebesgue space is studied.