On a Riemann boundary value problem for weighted spaces in the half-plane

Abstract

The paper considers the Riemann boundary value problem in the half-plane in the class of functions that are $C(\rho)$-continuous with respect to the weight $\rho(x)$, when the weight function has infinite number of zeros. Necessary and sufficient conditions for solvability of the problem are established. If the problem is solvable, solutions are represented in an explicit form.

Keywords

• Riemann boundary value problem
• weighted space
• factorization
• homogeneous problem
• Sokhotski-Plemelj formula