  In this paper we establish optimal local and global Besov-Lipschitz and
Triebel-Lizorkin estimates for the solutions to linear hyperbolic partial
differential equations. These estimates are based on local and global estimates
for Fourier integral operators that span all possible scales (and in particular
both Banach and quasi-Banach scales) of Besov-Lipschitz spaces
$B^s_{p,q}(\R^n)$, and certain Banach and quasi-Banach scales of
Triebel-Lizorkin spaces $F^s_{p,q}(\R^n)$
