On the boundedness of certain bilinear Fourier integral operators

Details On the boundedness of certain bilinear Fourier integral operators On the boundedness of certain bilinear Fourier integral operators

2011-11-20

arxiv.org/abs/1111.4653v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

We prove the global $L^2 \times L^2 \to L^1$ boundedness of bilinear Fourier integral operators with amplitudes in $S^0_{1,0} (n,2)$. To achieve this, we require that the phase function can be written as $(x,\xi,\eta) \mapsto \phase_1(x,\xi) + \phase_2(x,\eta)$ where each $\phase_j$ belongs to the class $\Phi^2$ and satisfies the strong non-degeneracy condition. This result extends that of R. Coifman and Y. Meyer regarding pseudodifferential operators to the case of Fourier integral operators.

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