Hardy spaces of harmonic quasiconformal mappings and Baernstein's theorem

Let S H 0 ( K ) , K ≥ 1 , be the class of normalized K -quasiconformal harmonic mappings in the unit disk. We obtain Baernstein type extremal results for the analytic and co-analytic parts of functions in the geometric subclasses of S H 0 ( K ) . We then apply these results to obtain integral means estimates for the respective classes. Furthermore, we find the range of p > 0 such that these geometric classes of harmonic quasiconformal mappings are contained in the Hardy space h p , thereby refining some earlier results of Nowak.