What question did this study set out to answer?

To establish sharp inequalities for the Fourier transform of the characteristic function of l^{p} balls and their implications for lattice point discrepancies.

April 18, 2026Journal of Inequalities and Applications0 citationsOpen Access

Sharp Fourier inequalities and lattice point discrepancy for l^p-balls

MLMartin LindKarlstad University

Puntos clave

To establish sharp inequalities for the Fourier transform of the characteristic function of l^{p} balls and their implications for lattice point discrepancies.
Analyzed the Fourier transform of the characteristic function for l^{p} balls in eal number spaces.
Derive bounds and asymptotic behaviors as p approaches 1 from the right.
Investigated lattice point discrepancy for dilates of l^{p} balls.
The supremum of the Fourier transform approaches as eal p approaches 1+.
Inequalities show that the Fourier transform of the characteristic function asymptotically behaves inversely with respect to (p-1).
Corresponding bounds for lattice point discrepancies were derived successfully.

Resumen

Abstract For 1 1 p ≤ 2, we establish sharp inequalities for the Fourier transform of the characteristic function of the l^p l p -unit ball B₏ R^2 B p ⊂ R 2. We show that ₑ^₂\|\|₂^3/2| ₁_₏ () | (p-1) ^-1/2 as p 1+ sup ω ∈ R 2 ∥ ω ∥ 2 3 / 2 | χ B p ˆ (ω) | ≍ (p − 1) − 1 / 2 as p → 1 + As an application, we obtain corresponding bounds for lattice point discrepancy inequalities for dilates of B₏ B p.

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