A Seeger-Sogge-Stein theorem for bilinear Fourier integral operators

2014/02/07 by Salvador Rodríguez-López, David Rule, Rodríguez-López, Salvador +3
Mathematics · #35S30 #42B20 #42B99 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1402.1729

openalex publication_date 2014/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the regularity of bilinear Fourier integral operators with bilinear amplitudes in S^m_1,0 (n,2) and non-degenerate phase functions, from L^p × L^q → L^r under the assumptions that m≤ -(n-1)(|(1)/(p)-(1)/(2)|+|(1)/(q)-(1)/(2)|) and (1)/(p)+(1)/(q)=(1)/(r). This is a bilinear version of the classical theorem of Seeger-Sogge-Stein concerning the L^p boundedness of linear Fourier integral operators. Moreover, our result goes beyond the aforementioned theorem in that it also includes the case of non-Banach target spaces.

Citations

• Multilinear Calderón–Zygmund Theory
• Hp spaces of several variables
• Some Maximal Inequalities

Related

• On the boundedness of certain bilinear Fourier integral operators
• Estimates for a certain bilinear Fourier integral operator
• Estimates for some bilinear wave operators
• L^p-boundedness of multi-parameter Fourier integral operators
• Notes on Regularity of Fourier integral operators with symbol in S^m_0,δ