An Approximate Inverse Riesz-Sobolev Inequality

Abstract

The Riesz-Sobolev inequality relates the convolution of nonnegative functions on Euclidean space to the convolution of their symmetric nonincreasing rearrangements. We show that for dimension one, for indicator functions of sets, if the inequality is sufficiently close to an equality then the sets in question must nearly coincide with intervals.

References in corpus (1)

• Near-extremizers of Young's inequality for discrete groups

Cited by in corpus (7)

• Near Equality in the Brunn-Minkowski Inequality
• Near-extremizers of Young's Inequality for R^d
• Near equality in the two-dimensional Brunn-Minkowski inequality
• A sharpened Riesz-Sobolev inequality
• A robust version of Freiman's $3k-4$ Theorem and applications
• Cases of equality in certain multilinear inequalities of Hardy-Riesz-Brascamp-Lieb-Luttinger type
• An inverse theorem for an inequality of Kneser