Iterated trilinear Fourier integrals with arbitrary symbols

作者：Jung Joeun^*

来源：Journal of Functional Analysis, 2017, 273(10): 3027-3060.

DOI：10.1016/j.jfa.2017.07.005

• Fourier analysis
• Multilinear operators
• Singular integral operators
• Time-frequency analysis

We prove L-P estimates for trilinear multiplier operators with singular symbols. These operators arise in the study of iterated trilinear Fourier integrals, which are trilinear variants of the bilinear Hilbert transform. Specifically, we consider trilinear operators determined by multipliers that are products of two functions m(1) (xi(1), xi(2)) and m(2) (xi(2), xi(3)), such that the singular set of m(1) lies in the hyperplane xi(1) = xi(2) and that of m(2) lies in the hyperplane xi(2) = xi(3). While previous work [8] requires that the multipliers satisfy chi xi(1)<xi(2) . chi xi(2)<xi(3) our results allow for the case of the arbitrary multipliers, which have common singularities.

• 出版日期2017-11-15