  While the local $L^p$-boundedness of nondegeneral Fourier integral operators
is known from the work of Seeger, Sogge and Stein, not so many results are
available for the global boundedness on $L^p(\mathbb R^n)$. In this paper we
give a sufficient condition for the global $L^p$-boundedness for a class of
Fourier integral operators which includes many natural examples. We also
describe a construction that can be used to deduce global results from the
local ones. An application is given to obtain global $L^p$-estimates for
solutions to Cauchy problems for hyperbolic partial differential equations.
