Abstract
We study the lattice bump multiplier problem. Precisely, given a smooth bump supported in a ball centered at the origin, we consider the multiplier formed by adding the translations of this bump centered at N distinct lattice points.
We investigate the dependence on N of the Lp norm of the linear and bilinear operators associated with this multiplier. We obtain sharp dependence on N in the linear case and in the bilinear case when p > 1.