Riemann problem for multiply connected domain in Besov spaces

Abstract

Abstract In this paper, we obtain conditions of the solvability of the Riemann boundary value problem for sectionally analytic functions in multiply connected domains in Besov spaces embedded into the class of continuous functions. We indicate a new class of Cauchy-type integrals, which are continuous on a closed domain with continuous (not Hölder) density in terms of Besov spaces, and for which the Sokhotski–Plemelj formulas are valid.

Keywords

• Riemann boundary value problem
• Sectionally analytic functions
• Cauchy-type integral
• Besov spaces