Riemann boundary value problem on quasidisks, Faber isomorphism and Grunsky operator
Let \(\Gamma\) be a bounded Jordan curve in the complex plane. The authors prove that the Plemelj-Sokhotski jump decomposition is an isomorphism if and only if \(\Gamma\) is a quasicircle. They also show that the Bergman space of \(L^2\) harmonic one-forms is isomorphic to the direct sum of the holomorphic Bergman spaces if and only if \(\Gamma\) is quasicircle, and obtain new interpretations of the Grunsky and Schiffer operators.
scientific article; zbMATH DE number 6837876
scientific article