Locally dened operators in the space of functions of bounded -variation

• Wadie Aziz Universidad de los Andes
• Jose A. Guerrero Instituto Superior de Formacion Docente Salome Ure~na Recinto Luis Napoleon Nuñez Molina
• Newman Zambrano Instituto Superior de Formacion Docente Salome Ure~na Recinto Luis Napoleon Nuñez Molina

Palabras clave: Function of bounded -variation, local operator, Nemytskii operator, continuous function

Resumen

We prove that every locally dened operator mapping the space of continuous and bounded -variation functions into itself is a Nemytskii composition operator.

Citas

L. Anzola, N. Merentes and J. L. Sanchez. Uniformly continuous composition operator in the space of -variation functions in the sense of Waterman. Submitted.

J. Appell and P. P. Zabrejko. Nonlinear superposition operators. Cambridge-Port Chester-Melbourne-Sydney, 1990.

W. Aziz, J. A. Guerrero, K. Maldonado and N. Merentes. Locally dened operators in thespace of continuous functions of bounded Riesz-variation, Journal of Mathematics, Volume

, Article ID 925091, http://dx.doi.org/10.1155/2015/925091.

K. Lichawski, J. Matkowski and J. Mis. Locally dened operators in the space of dierentiable functions. Bull. Pol. Acad. Sci. Math., 37 (1989), 315{325.

J. Matkowski and M. Wrobel. Locally dened operators in the space of Whitney dierentiable functions. Nonlinear Anal., 68 (2008), 2873{3232.

J. Matkowski and M. Wrobel. Representation theorem for locally dened operators in the space of Whitney dierentiable functions. Manuscripta Math., 129 (2009), 437{448.

J. Matkowski and M. Wrobel. The bounded local operators in the Banach space of Holder functions. Jan D lugosz University in Czestochowa, Scientic Issues, Mathematics XV (2010),

{98.

D. Waterman. On convergence of Fourier series of functions of generalized variation. Studia Math., 44 (1972), 107{117.

M. Wrobel. Locally dened operators and a partial solution of a conjecture. Nonlinear Anal., 72 (2010), 495{506.

M. Wrobel. Representation theorem for local operators in the space of continuous and monotone functions. J. Math. Anal. Appl., 372 (2010), 45{54.

M. Wrobel. Locally dened operators in the Holder's spaces. Nonlinear Anal., 74 (2011), 317{323.

M. Wrobel. Locally dened operators in the space of functions of bounded '-variation. Real Anal. Exch., 38(1) (2013), 79{94.