A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality
A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality
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.
12 pages; contribution to a volume dedicated to D. E. Edmunds and W. D. Evans; typo corrected in equation (1.3)
- California Institute of Technology United States
- College of New Jersey United States
Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, 330, Sobolev inequality, FOS: Mathematics, Hardy–Littlewood–Sobolev inequality, Sharp constants, 004, Functional Analysis (math.FA), Analysis of PDEs (math.AP)
Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, 330, Sobolev inequality, FOS: Mathematics, Hardy–Littlewood–Sobolev inequality, Sharp constants, 004, Functional Analysis (math.FA), Analysis of PDEs (math.AP)
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