Grunsky Operators And Quasiconformal Extensions For Univalent Functions

This paper deals mainly with the Grunsky functional g(f) and quasiconformal ex-tensions for a univalent function f. From functional analysis theory, we may introducea linear operator B on the complex Hilbert space l~2 with‖B‖=g(f). By consideringsome relations deduced from the the Grunsky inequality, we obtain some results on theGrunsky functional g(f) and its relation with extremal extensions of f.