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.

In this paper we study Vainikko integral operators which are similar to so-called cordial integral operators and contain the classical Hardy operator, the Schur operator, and the Hilbert transform as special cases. For such operators we obtain norm estimates and equalities, mainly in BV type spaces in the sense of Jordan, Wiener, Riesz, and Waterman. Several examples are also discussed.

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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