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

作者：Rodriguez Lopez Salvador; Rule David; Staubach Wolfgang^*

来源：Advances in Mathematics, 2014, 264: 1-54.

DOI：10.1016/j.aim.2014.07.009

• Bilinear Fourier integral operators
• Frequency space localisation

We establish the regularity of bilinear Fourier integral operators with bilinear amplitudes in S-1,0(m) (n, 2) and non-degenerate phase functions, from L-P x L-q -> L-r under the assumptions that m <= -(n - 1)(vertical bar 1/p - 1/2 vertical bar + vertical bar 1/q - 1/2 vertical bar) 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 quasi-Banach target spaces.

• 出版日期2014-10-20