# Some Remarks on Multiplier Spaces I: Classical Spaces

### Daria Bugajewska

Adam Mickiewicz University of Poznan, Poland### Simon Reinwand

Universität Würzburg, Germany

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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.

## Cite this article

Daria Bugajewska, Simon Reinwand, Some Remarks on Multiplier Spaces I: Classical Spaces. Z. Anal. Anwend. 38 (2019), no. 2, pp. 125–142

DOI 10.4171/ZAA/1631