Harmonic extensions of quasisymmetric mappings

Abstract

Let y be a quasisymmetr~c automorphism of the unit circle and P y its Poisson extension to the unit disk A. Various properties of P y are established. Hyperbolic and euclidean distance, between E y ( z ) and P,(z), z E A, are estimated, where E y is the Douady-Earle quasiconformal extension of y to A.