BOUNDARY CORRESPONDENCE UNDER HARMONIC QUASICONFORMAL HOMEOMORPHISMS OF THE UNIT DISK

Abstract

Let f be a harmonic homeomorphism of the unit disk onto itself. The following conditions are equivalent: (a) f is quasiconformal; (b) f is bi-Lipschitz in the Euclidean metric; (c) the boundary function is bi-Lipschitz and the Hilbert transformation of its derivative is in L 1 .