A sharpened Riesz-Sobolev inequality

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.

References in corpus (4)

• An Approximate Inverse Riesz-Sobolev Inequality
• Near-extremizers of Young's Inequality for R^d
• On an extremization problem concerning Fourier coefficients
• Near equality in the Riesz-Sobolev inequality in higher dimensions

Cited by in corpus (6)

• A robust version of Freiman's $3k-4$ Theorem and applications
• A note on a theorem of M. Christ
• Maximizers of Rogers-Brascamp-Lieb-Luttinger functionals in higher dimensions
• Equality in Brascamp-Lieb-Luttinger Inequalities
• A stability result for Riesz potentials in higher dimensions
• A Sharpened Rearrangement Inequality for Convolution on the Sphere