Pointwise regularity associated with function spaces and multifractal analysis
The purpose of multifractal analysis of functions is to determine the Hausdorff dimensions of the sets of points where a function (or a distribution) f has a given pointwise regularity exponent H. This notion has many variants depending on the global hypotheses made on f; if f locally belongs to a Banach space E, then a family of pointwise regularity spaces are constructed, leading to a notion of pointwise regularity with respect to E; the case corresponds to the usual Hölder regularity, and...