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arXiv · 2605.03732

Sharp Stability for the Affine Fractional Sobolev Inequality

Song Fan·Gui-Dong Li·Jianjun Zhang
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Abstract

In this paper, we prove a sharp quantitative stability result for the affine fractional \(L^2\)-Sobolev inequality in \(\dot H^s(\mathbb R^n)\), \(0<s<1\), introduced by Haddad--Ludwig (\emph{Math. Ann.} \textbf{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.

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Song Fan, Gui-Dong Li, Jianjun Zhang. 2026-05-05. Sharp Stability for the Affine Fractional Sobolev Inequality. https://arxiv.org/abs/2605.03732

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