Riemann boundary value problem on quasidisks, Faber isomorphism and Grunsky operator (Q682077)

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.