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

Published 27 Oct 2010 in math.FA and math.AP | (1010.5821v3)

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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