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

Authors

  • René Erlín Castillo Castillo Universidad Nacional de Colombia.
  • Nelson Merentes Universidad Central de Venezuela
  • Eduard Trousselot Universidad de Oriente.

DOI:

https://doi.org/10.4067/S0716-09172013000200003

Keywords:

(p, α)-variation, Nemytskii operator.

Abstract

We introduce the notion of bounded Φ-variation in the sense of LΦ-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 ∈ [0, 2π], y ∈ R.

References

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How to Cite

[1]
R. E. Castillo Castillo, N. Merentes, and E. Trousselot, “The Nemytskii operator on bounded Φ-variation in the mean spaces”, Proyecciones (Antofagasta, On line), vol. 32, no. 2, pp. 119-142, 1.

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