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

RENE E. CASTILLO, NELSON MERENTES, EDUARD TROUSSELOT

Resumen


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

Palabras clave


(p, α)-variation ; Nemytskii operator.

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172013000200003

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