Global boundedness of multilinear Fourier integral operators

Details Global boundedness of multilinear Fourier integral operators Global boundedness of multilinear Fourier integral operators

2011-11-20

arxiv.org/abs/1111.4652v2

Mathematics

Analysis of PDEs

35 pages

Scientific paper

We study the global boundedness of bilinear and multilinear Fourier integral operators on Banach and quasi-Banach $L^p$ spaces, where the amplitudes of the operators are smooth or rough in the spatial variables. The results are obtained by proving suitable global boundedness of rough linear Fourier integral operators with amplitudes that behave as $L^{p}$ functions in the spatial variables. The bilinear and multilinear boundedness estimates are proven by using either an iteration procedure or decomposition of the amplitudes, and thereafter applying our global results for linear Fourier integral operators with rough amplitudes.

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