%0 Journal Article
%T On Functions of Bounded -Variation
%A N. Merentes
%A S. Rivas
%A J. L. Sanchez
%J Journal of Function Spaces and Applications
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/202987
%X We introduce and study the concept of (,)-variation (1<<¡Þ, ¡Ê£¿) of a real function on a compact interval. In particular, we prove that a function ¡Ã[,]¡ú£¿ has bounded (,)-variation if and only if (£¿1) is absolutely continuous on [,] and () belongs to [,]. Moreover, an explicit connection between the (,)-variation of  and the -norm of () is given which is parallel to the classical Riesz formula characterizing functions in the spaces [,] and [,]. This may also be considered as an alternative characterization of the one variable Sobolev space [,].
%U http://www.hindawi.com/journals/jfsa/2012/202987/