On asymptotic symmetry under quasiconformal mappings (Q1385948)

It is a well-known result from \textit{A. Beurling} and \textit{L. Ahlfors} [Acta Math. 96, 125-142 (1956; Zbl 0072.29602)] that a homeomorphism \(h\) of the real axis onto itself is quasisymmetric if and only if there exists a quasiconformal extension of \(h\) to the upper half-plane. This paper deals with properties of the quasisymmetric boundary values \(h\) of a quasiconformal mapping of the upper half-plane onto itself depending on the behavior of complex dilatation.