Sharp Stability for the Affine Fractional Sobolev Inequality

2026/05/05 by Song Fan, Gui-Dong Li, Jianjun Zhang · 1 citation
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Abstract

In this paper, we prove a sharp quantitative stability result for the affine fractional \(L²\)-Sobolev inequality in \( H^s(\mathbb Rⁿ)\), \(0<s<1\), introduced by Haddad--Ludwig (Math. Ann. 388 (2024), 1091--1115). In particular, we identify the kernel of the affine Hessian, determine the sharp local spectral gap, and show that the optimal global stability constant is strictly smaller than the corresponding local spectral value.

Citations

• Sharp Quantitative Stability for the Affine \(p\)-Sobolev Inequality, Part I: The Case \(2≤ p<n\)

Cited by

• Sharp Quantitative Stability for the Affine \(p\)-Sobolev Inequality, Part I: The Case \(2≤ p<n\)

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