Pitt's inequality with sharp convolution estimates

2006/12/18 by William Beckner, Beckner, William · 3 citations
Mathematics · #35A15 #42B10 #58J70 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.math/0612486

openalex publication_date 2006/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sharp L^p 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 L^p to itself, and new proofs are given for the classical Pitt and Stein-Weiss estimates.

Cited by

• On a fuzzy Landau Equation: Part II. Solvability results
• Extremizers for a trilinear Stein-Weiss inequality with nonnegative weights
• Shifted Pitt and uncertainty inequalities on Riemannian symmetric spaces of noncompact type

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