The lattice bump multiplier problem
Volume 262 / 2022
Studia Mathematica 262 (2022), 225-240
MSC: Primary 42A45; Secondary 42B15, 42B25.
DOI: 10.4064/sm201219-18-4
Published online: 30 August 2021
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 $L^p$ 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 $p \gt 1$.
