Pitt's inequality with sharp convolution estimates
Abstract
Description
Sharp $L^p$ 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 $L^p$ to itself, and new proofs are given for the classical Pitt and Stein-Weiss estimates.
v.2 Added referenes, new results on logarithmic uncertainty, gradient estimates and mixed homogeneity, and corrected misprints. 12 pages, amslatex
v.2 Added referenes, new results on logarithmic uncertainty, gradient estimates and mixed homogeneity, and corrected misprints. 12 pages, amslatex