Sharp Stability for the Affine Fractional Sobolev Inequality
arXiv:2605.03732
summary
The paper proves a precise quantitative stability result for an affine fractional Sobolev inequality, identifying key spectral properties and showing the optimal global stability constant is smaller than the local spectral gap.
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.
Topics & keywords
#fractional sobolev inequalities#affine analysis#stability estimates#spectral gap#functional inequalitiesaffine fractional Sobolev inequalitysharp stabilityaffine Hessianspectral gapdot H^s