Pitt's inequality and the fractional Laplacian: sharp error estimates
Analysis of PDEs
2009-07-31 v6
Abstract
Sharp error estimates in terms of the fractional Laplacian and a weighted Besov norm are obtained for Pitt's inequality by using the spectral representation with weights for the fractional Laplacian due to Frank, Lieb and Seiringer and the sharp Stein-Weiss inequality. Dilation invariance, group symmetry on a non-unimodular group and a nonlinear Stein-Weiss lemma are used to provide short proofs of the Frank-Seiringer "Hardy inequalities" where fractional smoothness is measured by a Besov norm.
Keywords
Cite
@article{arxiv.math/0701939,
title = {Pitt's inequality and the fractional Laplacian: sharp error estimates},
author = {William Beckner},
journal= {arXiv preprint arXiv:math/0701939},
year = {2009}
}
Comments
v.6. Added new results extending estimates for fractional smoothness to the Heisenberg group and product spaces with mixed homogeneity. 25 pages, AMSLaTeX