Abstract
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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Communicated by M.Struwe.
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Frank, R.L., Lieb, E.H. Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality. Calc. Var. 39, 85–99 (2010). https://doi.org/10.1007/s00526-009-0302-x
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DOI: https://doi.org/10.1007/s00526-009-0302-x