On the Global Boundedness of Fourier Integral Operators

@inproceedings{Cordero2008OnTG,
  title={On the Global Boundedness of Fourier Integral Operators},
  author={Elena Cordero and Fabio Nicola and Luigi Rodino},
  year={2008}
}
We consider a class of Fourier integral operators, globally defined on R, with symbols and phases satisfying product type estimates (the so-called SG or scattering classes). We prove a sharp continuity result for such operators when acting on the modulation spaces M. The minimal loss of derivatives is shown to be d|1/2−1/p|. This global perspective produces a loss of decay as well, given by the same order. Strictly related, striking examples of unboundedness on L spaces are presented. 

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