Composition operators on weighted Bergman spaces of Dirichlet series

We study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some specific cases, upper and lower bounds of the essential norm of these operators and a criterion of compactness on classicals weighted Bergman spaces. Moreover, a sufficient condition of compactness is obtained using the notion of Carleson's measure

Isometric and invertible composition operators on weighted Bergman spaces of Dirichlet series

We show that a composition operator on weighted Bergman spaces $\mathcal{A}_{\mu}^p$ is invertible if and only if it is Fredholm if and only if it is an isometry

A flow-based approach to rough differential equations

These are lecture notes for a Master 2 course on rough differential equations driven by weak geometric Holder p-rough paths, for any p>2. They provide a short, self-contained and pedagogical account of the theory, with an emphasis on flows. The theory is illustrated by some now classical applications to stochastic analysis, such as the basics of Freidlin-Wentzel theory of large deviations for diffusions, or Stroock and Varadhan support theorem.Comment: 63 page