On the Nevanlinna's Theory for Vector-Valued Mappings

Abstract

The purpose of this paper is to establish the first and second fundamental theorems for anE-valued meromorphic mapping from a generic domainD⊂ℂto an infinite dimensional complex Banach spaceEwith a Schauder basis. It is a continuation of the work of C. Hu and Q. Hu. Forf(z)defined in the disk, we will prove Chuang's inequality, which is to compare the relationship betweenT(r,f)andT(r,f′). Consequently, we obtain that the order and the lower order off(z)and its derivativef′(z)are the same.