On the global boundedness of Fourier integral operators

By Elena Cordero, Fabio Di Nicola, L. Rodino. 2008

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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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aef1e6cb84277f6fa76902ce2b36598a432fea05