A sharpened Riesz-Sobolev inequality

2017/06/06 by Michael Christ, Christ, Michael · 3 citations
Mathematics · #Numerical methods in inverse problems #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1706.02007

Abstract

The Riesz-Sobolev inequality provides an upper bound, in integral form, for the convolution of indicator functions of subsets of Euclidean space. We formulate and prove a sharper form of the inequality. This can be equivalently phrased as a stability result, quantifying an inverse theorem of Burchard that characterizes cases of equality.

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• Equality in Brascamp-Lieb-Luttinger Inequalities
• A Sharpened Rearrangement Inequality for Convolution on the Sphere
• A stability result for Riesz potentials in higher dimensions

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