Near-extremizers of Young's Inequality for R^d

Details Near-extremizers of Young's Inequality for R^d Near-extremizers of Young's Inequality for R^d

2011-12-20

arxiv.org/abs/1112.4875v1

Mathematics

Classical Analysis and ODEs

Scientific paper

If a pair of functions nearly extremizes Young's convolution inequality for
R^d, with all three exponents finite and strictly greater than 1, then each
function is close in norm to a Gaussian. The proof relies on the Riesz-Sobolev
rearrangement inequality and in particular, on an approximate inverse
Riesz-Sobolev inequality established in a companion paper.

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