A calculus of Fourier integral operators with inhomogeneous phase functions on R (d)

We construct a calculus for generalized SG Fourier integral operators, extending known results to a broader class of symbols of SG type. In particular, we do not require that the phase functions are homogeneous. An essential ingredient in the proofs is a general criterion for asymptotic expansions within the Weyl- Hörmander calculus, which we previously proved. We also prove the L^2(R^d)-boundedness of the generalized SG Fourier integral operators having regular phase functions and uniformly bounded amplitudes.