Some Remarks on Multiplier Spaces I: Classical Spaces

Abstract

The aim of this note is to characterize the multiplier class $X/Y$ of functions $g$ such that $fg$ belongs to $X$ whenever $f$ belongs to $Y$ for certain given classes $X$ and $Y$ of real valued functions on [0, 1]. This paper is the first of two connected parts and deals with classical spaces $X$ and $Y$ of continuous, bounded and Darboux functions, as well as functions of bounded variation in the sense of Jordan and functions which have a primitive. Moreover, we give a new and elementary proof for the fact that $D/D$ contains only constant functions.