Resumen de Paraproduit sur le groupe de Heisenberg et applications
Isabelle Gallagher, Hajer Bahouri
We adapt the homogeneous Littlewood-Paley decomposition on the Heisenberg group constructed by H. Bahouri, P. Gérard et C.-J. Xu in [4] to the inhomogeneous case, which enables us to build paraproduct operators, similar to those defined by J.-M. Bony in [5]; although there is no simple formula for the Fourier transform of the product of two functions, some spectral localization properties of the classical case are preserved on the Heisenberg group after the product has been taken. Using the dyadic decomposition and the paraproduct algorithm, we prove the Gagliardo-Nierenberg inequality on the Heisenberg group; the smoothness of solutions of subelliptic, semi-linear systems is also studied, as well as semi-linear wave equations.
