Quasiconformality of harmonic extensions

Continued from Partyka and Sakan (Bull. Soc. Sci. Letters Lódź 47 (1997) 51–63) this paper aims at giving necessary and sufficient conditions on sense-preserving homeomorphisms of the unit circle for the quasiconformality of their harmonic extensions to the unit disk. In particular, all such homeomorphisms with a bounded derivative are well characterized. In consequence, a generalization of Martioʹs result is obtained.