Some properties of multipliers of summable derivatives (Q1071119)

If F is an arbitrary class of functions transforming the unit interval into real numbers, then M(F) denotes the system of all real functions f defined on the unit interval such that \(fg\in F\) for each \(g\in F.\) The functions in M(F) are called multipliers of F. The problem of characterizing of the system M (summable derivatives) has been solved by the author in Real Anal. Exch. 8, 486-493 (1983; Zbl 0554.26004). The main result of this paper states that the set of points of discontinuity of a function in M(SD), where SD is the class of all summable \((=Lebesgue\) integrable) derivatives, is countable and nowhere dense and that there exists a continuous function belonging to M(SD) which is nowhere differentiable.