Proyecciones Journal of Mathematics Vol. 32, N^o 2, pp. 119-142, June 2013. Universidad Católica del Norte Antofagasta - Chile

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

René Erlin Castillo

Universidad Nacional de Colombia, Colombia

Nelson Merentes

Universidad Central de Venezuela, Venezuela

Eduard Trousselot

Universidad de Oriente,

Venezuela

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ABSTRACT

We introduce the notion of bounded Ö-variation in the sense of L_Ö-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.

2000 Mathematics Subject Classification : Primary 26A45, 26B30; Secundary: 26A16, 26A24.

Key Words : (p, á)-variation, Nemytskii operator.

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REFERENCES

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Rene Erlin Castillo
Departamento de Matemáticas, Universidad Nacional de Colombia,
Ciudad Universitaria: Carrera 30, Calle 45, Bogotáa, Colombia
e-mail : recastillo@unal.edu.co

Nelson Merentes
Departamento de Matemáaticas, Universidad Central de Venezuela Caracas,
Venezuela
e-mail : nmerucv@gmail.com

Eduard Trousselot
Departamento de Matemaáticas, Universidad de Oriente
6101 Cumanáa, Edo. Sucre, Venezuela
e-mail : eddycharles2007@hotmail.com

 

Received : November 2011. Accepted : April 2013