For 1 < p <= 2, we establish sharp inequalities for the Fourier transform of the characteristic function of the l(p)-unit ball B-p subset of & Ropf;(2). We show that sup (omega is an element of & Ropf;2) parallel to omega parallel to(3/2) (2) |chi Bp (omega)| asymptotic to (p - 1)(-1/2) as p -> 1+ As an application, we obtain corresponding bounds for lattice point discrepancy inequalities for dilates of B-p.