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

• Published in: Journal of inequalities and applications Vol. 2020; no. 1; pp. 1 - 14
• Main Author: Pingrun Li
• Format: Journal Article
• Language: English
• Published: SpringerOpen 01-10-2020
• Subjects: Canonical function; Function spaces H ∗ $H_{\ast }; Riemann–Hilbert problems; Singular integral equations; Sokhotski–Plemelj formula
• ISSN: 1029-242X
• DOI: 10.1186/s13660-020-02501-x

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.