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

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.

arXiv comment12 pages; contribution to a volume dedicated to D. E. Edmunds and W. D. Evans; typo corrected in equation (1.3)