Schwarz-Pick Estimates for Holomorphic Mappings with Values in Homogeneous Ball

Abstract

Let BX be the unit ball in a complex Banach space X. Assume BX is homogeneous. The generalization of the Schwarz-Pick estimates of partial derivatives of arbitrary order is established for holomorphic mappings from the unit ball Bn to BX associated with the Carathéodory metric, which extend the corresponding Chen and Liu, Dai et al. results.