Uniformly continuos superposition operators on spaces of functions of bounded variation defined on compact subset of C
Resumen
En este artículo mostramos que si la función generadora h de un operador de superposición H, es continua en la primera variable y si H envía un subconjunto del BV(s), el espacio de las funciones de variación acotada sobre subconjuntos compactos de C (el plano complejo), en otro espacio específico entonces la función generadora h es afín en la variable funcional.
Citas
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M. Wróbel, Locally defined operators in the H"'older spaces, Nonlinear Analysis: Theory, Methods and Applications, 74 (2011), 317- 323.
B. Ashton,, and l. Doust, Functions of bounded variation on compact subsets of the plane, Studia Math., 169 (2005), 163-188.
S.T. Chen, Geometry of Orlicz Spaces, Dissertationes Mathematicae (Rozprawy Matematyczne)356 (Polish Acad. Sci., Warsaw, 1996).
J. Giménez, N. Merentes and M. Vivas, Functions of bounded variation on compact subsets of C. (accepted for publication in Commentationes Mathematica)
M. Kuzcma, An introduction to the theory of functional Equations and Inequalities, Polish Scientific Editors and Silesian University, Warszawa, Kraków, katowice, 1985.
K. Lichawski , J. Matkowski , J. Mis, Locally defined operators in the space of differentiable functions, Bull. Polish Acad. Sci. Math. 37(1989), 315-125 .
A.Wawrzynczyk , Introducción al análisis funcional, Universidad Autónoma Metropolitana, Unidd Iztapalapa, 1993.
M.Wróbel, Representation theorern for local operators in the space of continuous and monotone functions, J. Math . Anal. Appl. 372 (2010), 45-54.
M. Wróbel, Locally defined operators in the H"'older spaces, Nonlinear Analysis: Theory, Methods and Applications, 74 (2011), 317- 323.
