Annals of Global Analysis and Geometry

, Volume 38, Issue 4, pp 373–398 | Cite as

On the global boundedness of Fourier integral operators

Original Paper


We consider a class of Fourier integral operators, globally defined on \({{\mathbb R}^{d}}\) , 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 Mp. 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 Lp spaces are presented.


SG-Fourier integral operators Modulation spaces Short-time Fourier transform 

Mathematics Subject Classification (2000)

35S30 47G30 42C15 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorinoTorinoItaly
  2. 2.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly

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