Lipschitz spaces and bounded mean oscillation of harmonic mappings

Abstract

We first study the bounded mean oscillation of planar harmonic mappings. Then we establish a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings. Finally, we obtain sharp estimates on the Lipschitz number of planar harmonic mappings in terms of the bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to BMO2 as a Banach space. © 2012 Australian Mathematical Publishing Association Inc.