Maximizers of the L2 → L4 Fourier extension inequality for cones in finite fields
Year: 2026
Type: article
Abstract: Sharp Fourier restriction inequalities in euclidean spaces and the restriction phenomenon in finite fields have both been topics of interest in the last few decades. Very recently, the research at the intersection of these two topics began. In [8] , it was established that, for the ( 3 , 1 ) -cone Γ ( 3 , 1 ) 3 : = { η ∈ F q 4 ∖ { 0 } : η 1 2 + η 2 2 + η 3 2 = η 4 2 } , the L 2 → L 4 Fourier extension inequality is saturated by constant functions when q = 3 ( mod 4 ) . In this manuscript, we advance this line of inquiry by establishing sharp forms of L 2 → L 4 Fourier extension inequalities for all the remaining cones Γ 3 ⊂ F q 4 . These cones include the ( 2 , 2 ) -cone Γ ( 2 , 2 ) 3 : = { η ∈ F q 4 ∖ { 0 } : η 1 2 + η 2 2 = η 3 2 + η 4 2 } for general q = p n and the ( 3 , 1 ) -cone when q = 1 ( mod 4 ) . Moreover, we classify all the extremizers in both cases. We note that the corresponding problem for the ( 2 , 2 ) -cone in the euclidean setting remains open.
Source: Journal of Functional Analysis
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,250
OpenAlex ID: W7140750737