Sharp quantitative stability is proved for the affine fractional L2-Sobolev inequality, identifying the affine Hessian kernel and showing the global stability constant is strictly smaller than the local spectral gap.
Lions, The concentration-compactness principle in the calculus of variations
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Sharp Stability for the Affine Fractional Sobolev Inequality
Sharp quantitative stability is proved for the affine fractional L2-Sobolev inequality, identifying the affine Hessian kernel and showing the global stability constant is strictly smaller than the local spectral gap.