  We study the boundedness of rough Fourier integral and pseudodifferential
operators, defined by general rough H\"ormander class amplitudes, on Banach and
quasi-Banach $L^p$ spaces. Thereafter we apply the aforementioned boundedness
in order to improve on some of the existing boundedness results for H\"ormander
class bilinear pseudodifferential operators and certain classes of bilinear (as
well as multilinear) Fourier integral operators. For these classes of
amplitudes, the boundedness of the aforementioned Fourier integral operators
turn out to be sharp. Furthermore we also obtain results for rough multilinear
operators.
