Work

Dimension‐free Fourier restriction inequalities

Year: 2025

Type: article

Abstract: Let denote the best constant for the Fourier restriction inequality to the unit sphere , and let denote the corresponding constant for radial functions. We investigate the asymptotic behavior of the operator norms and as the dimension tends to infinity. We further establish a dimension‐free endpoint Stein–Tomas inequality for radial functions, together with the corresponding estimate for general functions which we prove with an dependence. Our methods rely on a uniform two‐sided refinement of Stempak's asymptotic estimate of Bessel functions.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70098

Authors: Diogo Oliveira e Silva, Błażej Wróbel

Institutions: Instituto Superior Técnico, University of Wrocław, Institute of Mathematics, Polish Academy of Sciences

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Narodowym Centrum Nauki, Fundação para a Ciência e a Tecnologia

Awards: Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, EXC 2047: Hausdorff Center for Mathematics (HCM), G1600773818, G4255701961, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos