The de la Vallée-Poussin theorem and Orlicz spaces associated to a vector measure

Abstract

For a vector measure m, with values in a Banach space, we analyze the localization of uniformly integrable subsets of scalar integrable functions with respect to m in a suitable Orlicz space associated to m. As tools we consider the properties of Orlicz spaces associated to intermediate functions of a given pair of Young functions. These properties allow us to obtain compactness properties of the inclusion operators.