V. H. Nguyen

A Fourier approach to the sharp stability of Heisenberg Uncertainty Principles of higher and fractional orders: a new perspective

We show that, on the Fourier side, the sharp second order Heisenberg Uncertainty Principle (HUP) and its sharp stability for functions are nothing but the first order $L^{2}$-Caffarelli--Kohn--Nirenberg inequality and its sharp stability, applied to their Fourier transforms. This gives a proof in a few lines of the sha...