Sharp Pointwise Contraction of Mappings with Integrable Distortion Which Are Quasiconformal in a Disk

Abstract

We consider quasiconformal mappings of the unit disk that have a planar extension which have $p$-integrable distortion. In this paper, we establish a bound for the modulus of continuity for the inverse mapping and show sharpness of this bound. Furthermore, we also obtain bounds for the compression multifractal spectra of such mappings.