abstract: I will focus on para-products on particular Lie groups for which notions of Fourier transforms exist (H-type groups). I will define a Littlewood-Paley decomposition, Besov spaces.....as soon as I can I will generalize the results to groups with polynomial volume growth. On the other hand, I will introduce para-differential operators on Riemannian manifolds without using Fourier transform but harmonic analysis techniques and prove a para-linearisation theorem. I will apply it to the regularity of some PDE.
In collaboration within the ERC project GeMeThnES Grant Agreement n. 246923