On the boundedness of certain bilinear Fourier integral operators

Abstract

We prove the global $L^2\times L^2\to L^1$ boundedness of bilinear Fourier integral operators with amplitudes in $S_{1,0}^0(n,2)$. To achieve this, we require that the phase function can be written as $(x,ξ,η) \mapsto \phase_1(x,ξ) + \phase_2(x,η)$ 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.

arXiv comment20 pages

References in corpus (1)

• Global and local regularity of Fourier integral operators on weighted and unweighted spaces