The Nemytskii operator on bounded ö-variation in the mean spaces
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...
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| Autores principales: | , , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2013
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000200003 |
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| Sumario: | 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. |
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