Generalized Besov spaces : from uniform characterizations to pointwise applications

We will start the presentation by giving some alternative definitions for
the Besov spaces of generalized smoothness. In particular, links between those
spaces and Sobolev spaces will be explored. A generalized method of interpola-
tion will come out from this characterization.
Then, we will show how those spaces can help to determine the pointwise
regularity of some functions, using wavelet transform and the notion of preva-
lence.
Once done, links between this pointwise regularity and elliptic partial dif-
ferentiable equations will be discussed. This will generalize some results of
Calderón and Zygmund.