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arXiv · 0804.3928

On the global boundedness of Fourier integral operators

Elena Cordero·Fabio Nicola·Luigi Rodino
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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 $M^p$. 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 $L^p$ spaces are presented.

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Elena Cordero, Fabio Nicola, Luigi Rodino. 2008-04-24. On the global boundedness of Fourier integral operators. https://arxiv.org/abs/0804.3928

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