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math.FA2010
A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality
Rupert L. Frank, Elliott H. Lieb
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…
math.FA2010
Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality
Rupert L. Frank, Elliott H. Lieb
We introduce the concept of spherical (as distinguished from planar) reflection positivity and use it to obtain a new proof of the sharp constants in certain cases of the HLS and t…