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

Abstract

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