APDE seminar@BCAM: Every classical inequality for the Fourier operator is trivial

Abstract

In this talk we will see that if the Fourier operator is bounded between two classical spaces (for instance, rearrangement invariant spaces), then every operator which maps L^1 and L^2 to L^\infty and L^2, respectively, must also be bounded.  We will also discuss why this means that there cannot be any  "interesting"  classical Fourier inequalities and give some applications. Joint work with Sergey Tikhonov.