A constrained optimization problem for the Fourier transform: Quantitative analysis

Abstract

Among functions $f$ majorized by indicator functions $1_E$, which functions have maximal ratio $\Vert \hat{f}{\Vert }_q/|E{|}^{1/p}$? We establish a quantitative answer to this question for exponents $q$ sufficiently close to even integers, building on previous work proving the existence of such maximizers.

arXiv comment34 pages