Annals of Global Analysis and Geometry

, Volume 38, Issue 4, pp 373–398

On the global boundedness of Fourier integral operators

Authors

  • Elena Cordero
    • Department of MathematicsUniversity of Torino
    • Dipartimento di MatematicaPolitecnico di Torino
  • Luigi Rodino
    • Department of MathematicsUniversity of Torino
Original Paper

DOI: 10.1007/s10455-010-9219-z

Cite this article as:
Cordero, E., Nicola, F. & Rodino, L. Ann Glob Anal Geom (2010) 38: 373. doi:10.1007/s10455-010-9219-z

Abstract

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.

Keywords

SG-Fourier integral operatorsModulation spacesShort-time Fourier transform

Mathematics Subject Classification (2000)

35S3047G3042C15

Copyright information

© Springer Science+Business Media B.V. 2010