On generalized Hölder spaces

The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis and lead to natural definitions of the notion of fractal function; for example a function belonging to $C^\alpha$ with $\alpha\in (0,1)$ typically has a fractal graph. The purpose of this poster is to present a generalization of such spaces as well as some recent results about their characterizations.