On the boundedness of certain bilinear Fourier integral operators

2011/11/20 by Salvador Rodríguez-López, David Rule, Rodriguez-Lopez, Salvador +3
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1111.4653

openalex publication_date 2011/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the global L² × L² → L¹ boundedness of bilinear Fourier integral operators with amplitudes in S⁰_1,0 (n,2). To achieve this, we require that the phase function can be written as (x,ξ,η) ↦ \phase₁(x,ξ) + \phase₂(x,η) where each \phase_j belongs to the class Φ² 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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