Angular derivatives of quasiconformal harmonic maps on the Poincar, disk

摘要

Let be the boundary of the open unit disk and let h be a quasisymmetric homeomorphism from the unit circle onto itself. Let H be the quasiconformal harmonic extension of h to with respect to the Poincar, metric. In this paper, it is shown that, if at in , then when in non-tangentially, and the complex derivatives and approach and 0 respectively, i.e., H has an angular derivative at ; conversely, if H has a non-tangential derivative at , then and hence H has an angular derivative at .