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April 18, 2026Journal of Inequalities and Applications0 citationsOpen Access

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

MLMartin Lind

Key Points

  • 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.

Abstract

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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Cite This Study

Martin Lind (2026) studied this question.

synapsesocial.com/papers/69e3205140886becb653f695https://doi.org/10.1186/s13660-026-03476-x
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