Abstract
Abstract In this paper, we define a particular class of Fourier Integral Operators (FIO for short). These FIO turn out to be bounded on the spaces S (ℝ n ) of rapidly decreasing functions (or Schwartz space) and S′ (ℝ n ) of temperate distributions. Results about the composition of FIO with its L 2-adjoint are proved. These allow to obtain results about the continuity on the Sobolev Spaces.
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