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

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.