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

摘要

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-Hormander calculus. We also prove the L (2)(R (d) )-boundedness of the generalized SG Fourier integral operators having regular phase functions and amplitudes uniformly bounded on R (2d) .