Establish constructive stability for the sharpened Hausdorff–Young inequality

Establish a constructive stability inequality with quantitative control for the sharpened Hausdorff–Young inequality, including an explicit stability constant and an appropriate distance to its extremizer manifold.

Background

The paper develops effective global stability estimates for three even-exponent Schrödinger Strichartz inequalities by combining an explicit spectral gap with heat-flow monotonicity and a quantitative local Taylor estimate.

As a related comparison, the authors note that the sharpened Hausdorff–Young inequality has qualitative stability information but lacks a constructive, quantitative version. This is an independent unresolved problem mentioned to situate the paper’s effective stability results within the broader theory of sharp inequalities.

References

A similar situation underlies the sharpened Hausdorff--Young inequality of Christ , for which constructive stability is still an open question.

— Gaussians Do Not Always Maximize Mixed-Norm Strichartz Inequalities for the Schrödinger Equation  (2609.11644 - Gonçalves et al., 10 Sep 2026) in Section 1, subsection “Main results”