The Nemytskii operator on bounded p-variation in the mean spaces

We introduce the notion of bounded p-variation in the sense of Lp-norm. We obtain a Riesz type result for functions of bounded p-variation in the mean. We show that if the Nemytskii operator map the bounded p-variation in the mean spaces into itself and satisfy some Lipschitz condition there exist two functions g and h belonging to the bounded p-variation in the mean space such that f(t, y) = g(t)y + h(t), t 2 [0, 2pi], y 2 R.