Composition operators on Hardy-Sobolev spaces and $BMO$-quasiconformal mappings

Abstract

In this paper we consider composition operators on Hardy-Sobolev spaces in connections with BM O-quasiconformal mappings. Using the duality of Hardy spaces and BMO-spaces we prove that BM O-quasiconformal mappings generate bounded composition operators from Hardy-Sobolev spaces to Sobolev spaces.