The solvability of a kind of generalized Riemann–Hilbert problems on function spaces H ∗ $H_{\ast }$

Abstract

Abstract In this paper, we study a kind of generalized Riemann–Hilbert problems (R-HPs) with several unknown functions in strip domains. We mainly discuss methods of solving R-HPs with two unknown functions and obtain general solutions and conditions of solvability on function spaces H ∗ $H_{\ast }$ . At the end of this paper, we consider in detail the behavior of the solution at ∞ and in different domains. Thus the results in this paper generalize and improve the theory of the classical Riemann–Hilbert problems.

Keywords

• Riemann–Hilbert problems
• Singular integral equations
• Sokhotski–Plemelj formula
• Canonical function
• Function spaces H ∗ $H_{\ast }$