Operator Theory, Complex Analysis and Applications Seminar 

07/11/2014, 11:00 — 12:00 — Room P4.35, Mathematics Building
Abdelhamid Boussejra, University Ibn Tofail, Kenitra, Marocco

Poisson integrals on Riemannian Symmetric Spaces

In this talk we shall give characterizations of the $L^{p}$-range of the Poisson transform $P_{\lambda}$ associated to Riemannian Symmetric Spaces. We will focus on the rank one symmetric space case, and show that for $\lambda$ real, the Poisson transform is a bijection from the space of $L^{2}$ functions on the boundary (respectively $L^{p}$) onto a subspace of eigenfunctions of the Laplacian satisfying certain $L^{2}$-type norms (respectively Hardy-type norms).