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arXiv · 1010.5821

A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality

Rupert L. Frank·Elliott H. Lieb
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Abstract

We show that the sharp constant in the Hardy-Littlewood-Sobolev inequality can be derived using the method that we employed earlier for a similar inequality on the Heisenberg group. The merit of this proof is that it does not rely on rearrangement inequalities; it is the first one to do so for the whole parameter range.

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Rupert L. Frank, Elliott H. Lieb. 2012-05-03. A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. https://arxiv.org/abs/1010.5821

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