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Zeitschrift für Analysis und ihre Anwendungen

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Volume 38, Issue 2, 2019, pp. 125–142
DOI: 10.4171/ZAA/1631

Published online: 2019-04-09

Some Remarks on Multiplier Spaces I: Classical Spaces

Daria Bugajewska[1] and Simon Reinwand[2]

(1) Adam Mickiewicz University of Poznan, Poland
(2) Universität Würzburg, Germany

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.

Keywords: Bounded functions, continuous functions, Darboux functions, differentiable functions, multiplier set, variation in the sense of Jordan, Riesz, Waterman, Wiener, Young

Bugajewska Daria, Reinwand Simon: Some Remarks on Multiplier Spaces I: Classical Spaces. Z. Anal. Anwend. 38 (2019), 125-142. doi: 10.4171/ZAA/1631