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arXiv:math/0701939 [math.AP]AbstractReferencesReviewsResources

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

William Beckner

Published 2007-01-31, updated 2009-07-31Version 6

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.

Comments: v.6. Added new results extending estimates for fractional smoothness to the Heisenberg group and product spaces with mixed homogeneity. 25 pages, AMSLaTeX
Categories: math.AP
Subjects: 58J70, 42B10, 35A15
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