Pitt's inequality with sharp convolution estimates

Details Pitt's inequality with sharp convolution estimates Pitt's inequality with sharp convolution estimates

2006-12-18

arxiv.org/abs/math/0612486v2

Mathematics

Analysis of PDEs

v.2 Added referenes, new results on logarithmic uncertainty, gradient estimates and mixed homogeneity, and corrected misprints

Scientific paper

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.

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