Bounded variation space and the nemytskii operator

In the present paper, we give an overview on the basic properties of functions of bounded variation. We present a new proof of a type Riesz result for functions of bounded variation. Also, we show that if the Nemytskii operator maps the bounded variation space into itself and satisfies some Lipschitz condition, then there are two–functions g and h of bounded variation such that f(t,y) = g(t)y + h(t) for all t ∈ [a,b], y ∈ ℝ.