Pitt's inequality and the fractional Laplacian: sharp error estimates

Details Pitt's inequality and the fractional Laplacian: sharp error estimates Pitt's inequality and the fractional Laplacian: sharp error estimates

2007-01-31

arxiv.org/abs/math/0701939v6

Mathematics

Analysis of PDEs

v.6. Added new results extending estimates for fractional smoothness to the Heisenberg group and product spaces with mixed hom

Scientific paper

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.

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