Pitt's inequality with sharp convolution estimates
William Beckner
Abstract
Sharp Lp extensions of Pitt's inequality expressed as a weighted Sobolev inequality are obtained using convolution estimates and Stein-Weiss potentials. More generally, optimal constants are obtained for the full Stein-Weiss potential as a map from Lp to itself, and new proofs are given for the classical Pitt and Stein-Weiss estimates.
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