  Fourier integral operators with sufficiently smooth phase act on the
time-frequency content of functions. However time-frequency analysis has only
recently been used to analyze these operators. In this paper, we show that if a
Fourier integral operator has a smooth phase function and its symbol is
well-localized in time and frequency, then the operator is Schatten \( p
\)-class for \( p \in [1,2] \), with inclusion of the symbol in mixed
modulation spaces serving as the appropriate measure of time-frequency
localization. Our main results are sharp in the sense that larger mixed
modulation spaces necessarily contain symbols of Fourier integral operators
that are not Schatten \( p \)-class.
