New approach to affine Moser-Trudinger inequalities via Besov polar projection bodies

2024/05/12 by Óscar Domínguez, Yinqin Li, Dominguez, Oscar +7 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Metric Geometry (math.MG) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2405.07329

openalex publication_date 2024/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the affine inequalities on ℝⁿ for Sobolev functions in W^s,p with 1 ≤ p < n/s obtained recently by Haddad-Ludwig [16, 17] to the remaining range p ≥ n/s. For each value of s, our results are stronger than affine Moser-Trudinger and Morrey inequalities. As a byproduct, we establish the analog of the classical L^p Bourgain-Brezis-Mironescu inequalities related to the Moser-Trudinger case p=n. Our main tool is the affine invariant provided by Besov polar projection bodies.

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• Higher-order affine Sobolev inequalities

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