Abstract: Fourier multipliers appear often in in harmonic analysis and PDEs and their theory has found fruitful uses and applications. Bilinear Fourier multipliers appear when the product of frequencies of two functions is jointly altered by a symbol of two variables via multiplication. These multiplier operators share many features with their linear counterparts but also exhibit interesting behavior different from the linear case. In this talk we plan to discuss some properties of bilinear multipliers that diverge from the analogous linear ones. Results related to bilinear operators will also be presented. The talk is based on joint work with L. Grafakos, P. Honzik, and L. Slavikova.
