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arXiv · 1112.4875

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

Michael Christ
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Abstract

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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Michael Christ. 2011-12-20. Near-extremizers of Young's Inequality for R^d. https://arxiv.org/abs/1112.4875

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