ABSTRACT
This chapter begins a study of the functions that multiply Fα into itself. It focuses on the case when α is greater than 0. The chapter proves a basic sufficient condition for membership of a function Mα for the case when α is greater than zero and less than 1. This condition concerns the boundedness of certain weighted radial variations of the function. Some of these subsequent conditions rely on the basic condition given. Some facts about Mα hold in the more general setting of Banach spaces with additional properties described in the next lemma.
