Analysis on quasidisks: A unified approach through transmission and jump problems

Abstract

We give an exposition of results from a crossroad between geometric function theory, harmonic analysis, boundary value problems, and approximation theory, which characterize quasicircles. We will specifically expose the interplay between the jump decomposition, singular integral operators, approximation by Faber series, and the Grunsky inequalities. Our unified point of view is made possible by the concept of transmission.