Endpoint results for Fourier integral operators on noncompact symmetric   spaces
  Let X be a noncompact symmetric space of rank one and let h^1(X) be a local atomic Hardy space. We prove the boundedness from h^1(X) to L^1(X) and on h^1(X) of some classes of Fourier integral operators related to the wave equation associated with the Laplacian on X and we estimate the growth of their norms depending on time. 
Tommaso Bruno, Anita Tabacco, Maria Vallarino
math.FA