Factorization of entire mappings of nuclear bounded type

In this paper we study the relationships between the spaces of entire mappings of bounded type, entire mappings of nuclear bounded type, entire mappings of Pietsch integral bounded type, and entire mappings of Grothendieck integral bounded type. Several results due to Alencar (Proc. Roy. Irish Acad.85A (1985) 131–138) and Cilia and Gutiérrez (J. Aust. Math. Soc.76 (2004) 269–280) for homogeneous polynomials are extended to entire mappings. In the main result we prove that an entire mapping is of nuclear bounded type if and only if it factors through an entire mapping of Pietsch integral bounded type.