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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.
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