Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2019-07-15
Some Remarks on Multiplier Spaces II: BV-Type SpacesDaria Bugajewska and Simon Reinwand (1) Adam Mickiewicz University of Poznan, Poland
(2) Julius Maximilian Universität Würzburg, Germany
The aim of this note, which is a continuation of the article [Z. Anal. Anwend. 38 (2019), 125–142], is to characterize the multiplier classes $X/Y$ 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] of bounded variation. This paper is the second of two connected papers and deals with classes $X$ and $Y$ of functions of bounded variation in the sense of Young, Wiener, Waterman and Riesz, to which we also compare the classical spaces from the first part [Z. Anal. Anwend. 38 (2019), 125–142]. Moreover, we give some multiplier classes concerning related spaces like Lipschitz and absolutely continuous 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 II: BV-Type Spaces. Z. Anal. Anwend. 38 (2019), 309-327. doi: 10.4171/ZAA/1639