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Pitt's inequality and the fractional Laplacian: Sharp error estimates
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William Beckner
Published/Copyright:
January 19, 2012
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.: Fractional Laplacian; Sobolev inequalities
Received: 2009-06-05
Revised: 2010-03-09
Published Online: 2012-01-19
Published in Print: 2012-January
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Prelims
- The Lerch zeta function I. Zeta integrals
- The Lerch zeta function II. Analytic continuation
- Generalized Ramanujan conjecture over general imaginary quadratic fields
- Almost prime values of the order of elliptic curves over finite fields
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Manifolds associated with
- A Steinness criterion for Stein fibrations
- Crown-free highly arc-transitive digraphs
- Pitt's inequality and the fractional Laplacian: Sharp error estimates
- On affine group actions on Stein manifolds
