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

Abstract

We introduce the notion of bounded p-variation in the sense of [L.sub.p]-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 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 pertenece a [ 0, 2π ], y pertenece a R