Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

Details Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

2009-04-27

arxiv.org/abs/0904.4275v2

Calc. Var. Partial Differential Equations 39 (2010), no. 1 - 2, 85 - 99

Mathematics

Functional Analysis

15 pages; references added and minor changes

Scientific paper

We give a new proof of certain cases of the sharp HLS inequality. Instead of
symmetric decreasing rearrangement it uses the reflection positivity of
inversions in spheres. In doing this we extend a characterization of the
minimizing functions due to Li and Zhu.

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