An Approximate Inverse Riesz-Sobolev Inequality

Details An Approximate Inverse Riesz-Sobolev Inequality An Approximate Inverse Riesz-Sobolev Inequality

2011-12-16

arxiv.org/abs/1112.3715v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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