Generalized duality of some Banach function spaces

Abstract

The set of multipliers from one vector space to another vector space may be seen as a generalized dual space in the sense of Köthe. We give some properties of this kind of duality and prove precise estimates concerning generalized duality of X^P-spaces, Lebesgue, Lorentz, Marcinkiewicz and Orlicz spaces. We complement and unify several previous results of this kind.