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

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

2010-10-27

arxiv.org/abs/1010.5821v2

Mathematics

Functional Analysis

12 pages; contribution to a volume dedicated to D. E. Edmunds and W. D. Evans; minor additions

Scientific paper

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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