On The Compactness Of Grunsky Differential Operators

Grunsky operators play an important role in classical geometric function theory and in the study of Teichmuller spaces.The Grunsky map is known to be holomorphic on the universal Teichmuller space.In this thesis we shall deal with the compactness of a.Grunsky differential operator.We will give upper and lower estimates of the essen-tial norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator.