Exponentials rarely maximize Fourier extension inequalities for cones
Year: 2025
Type: article
Abstract: We prove the existence of maximizers and the precompactness of ‐normalized maximizing sequences modulo symmetries for all valid scale‐invariant Fourier extension inequalities on the cone in . In the range for which such inequalities are conjectural, our result is conditional on the boundedness of the extension operator. Global maximizers for the Fourier extension inequality on the cone in have been characterized in the lowest dimensional cases . We further prove that these functions are critical points for the to Fourier extension inequality if and only if .
DOI: 10.1112/jlms.70112
Institutions: Instituto Superior Técnico, University of Wisconsin–Madison
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,930
Awards: Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, EXC 2047: Hausdorff Center for Mathematics (HCM), G1600773818, CAREER: Degeneracies of Curvature in Harmonic Analysis, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, RTG: Analysis and Partial Differential Equations at the University of Wisconsin, Problems in Harmonic Analysis Relating to Curvature, G8321147636, Sharp Fourier Restriction Theory
OpenAlex ID: W4408260450