Study Of Variable Bounded Variation Spaces.

Under this project we intend to introduce and analyse the variable-$p$ version of the standard spaces of bounded variation functions in one variable, giving the right and basic definitions in order to such spaces work finely. One of the key points is to identify the basic properties of the variable function $p(x)$ that allow for these spaces to have reasonable properties. Another aim is to characterize the properties of this space, like completeness, separability and so forth.