Pitt's inequality with sharp convolution estimates
Analysis of PDEs
2007-05-23 v2
Abstract
Sharp 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 to itself, and new proofs are given for the classical Pitt and Stein-Weiss estimates.
Cite
@article{arxiv.math/0612486,
title = {Pitt's inequality with sharp convolution estimates},
author = {William Beckner},
journal= {arXiv preprint arXiv:math/0612486},
year = {2007}
}
Comments
v.2 Added referenes, new results on logarithmic uncertainty, gradient estimates and mixed homogeneity, and corrected misprints. 12 pages, amslatex