A sharpened Hausdorff-Young inequality

By Michael Christ. 2014

47 citations recorded by the source corpus.

The Hausdorff-Young inequality for Euclidean space, in its sharp form due to Beckner, gives an upper bound for the Fourier transform in terms of Lebesgue space norms, with an optimal constant. The extremizers have been identified by Lieb to be the Gaussians. We establish an improved upper bound, for functions that nearly extremize the inequality, with a negative second term roughly proportional to the square of the distance to the set of extremizers. One formulation of this term comes with its own sharp constant. The main step is to show that any extremizing sequence is precompact, modulo the action of the group of natural symmetries of the inequality. This step relies on inverse theorems of additive combinatorial nature.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e2362fe72198bfdf7e273d93dc95e6570871e3b3

How researchers see this paper

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In Applied Mathematics

1. Michael Loss
2. Rupert L. Frank
3. Jean Dolbeault
4. Maria J. Esteban
5. Alessio Figalli
6. Guido De Philippis
7. Van Hoang Nguyen
8. N. Fusco

In Discrete Mathematics and Combinatorics

1. Alessio Figalli

In Numerical Analysis

1. Rupert L. Frank
2. Alessio Figalli
3. Jean Dolbeault

Citations in the corpus

• Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (2022, background): “In fact, stability has attracted a lot of attention in recent years and we refer to [44, 26, 39, 27, 23, 30, 21, 24, 38, 25, 61, 42, 43, 40, 10] and the references within for a list of works in this direction.”