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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

CASTILLO, René Erlin; MERENTES, Nelson  and  TROUSSELOT, Eduard. The Nemytskii operator on bounded ö-variation in the mean spaces. Proyecciones (Antofagasta) [online]. 2013, vol.32, n.2, pp.119-142. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172013000200003.

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

Keywords : p, á)-variation; Nemytskii operator.

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