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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.32 no.2 Antofagasta May 2013

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

Proyecciones Journal of Mathematics Vol. 32, No 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


ABSTRACT

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.

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

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


REFERENCES

[1] Castillo R., The Nemytskii operator on bounded p-variation in the mean spaces, Matemticas: Enseanza Universitaria Vol XIX, N 1, pp. 31-41, (2011).

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[9] Mricz, F. and Siddiqi, A. H., A quatified version of the Dirichlet-Jordan test in L1-norm, Rend. Circ. Mat. Palermo, 45, pp. 19-24, (1996).

[10] Neves, M. T., Ö-variacin en el sentido de wiener y Riesz, Trabajo de pasanta (asesorado por S. Rivas) UNA Centro local Aragua, rea de Matemtica, Maracay, (1994).

[11] Riesz, F., Untersuchungen ber system intergrierbarer function, Math-ematische Annalen, 69, pp. 1449-1497, (1910).

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[13] Waterman, D., On Ë-Bounded Variation, Studia Mathematicae, LVII,pp. 33-45, (1976)

 

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

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