On the Compactness of Grunsky Differential Operators

Abstract

Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces. The Grunsky map is known to be holomorphic on the universal Teichmüller space. In this paper the authors deal with the compactness of a Grunsky differential operator. They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator.

Keywords

Universal Teichmüller space / Beltrami coefficient / Grunsky operator / Compact operator / p-Schatten class operator / Essential norm