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The lattice bump multiplier problem

Volume 262 / 2022

Eva Buriánková, Loukas Grafakos, Danqing He, Petr Honzík 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 $p \gt 1$.

Authors

  • Eva BuriánkováFaculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail
  • Loukas GrafakosDepartment of Mathematics
    University of Missouri
    Columbia, MO 65211, USA
    e-mail
  • Danqing HeSchool of Mathematical Sciences
    Fudan University
    220 Handan Road
    Shanghai 200433
    People’s Republic of China
    e-mail
  • Petr HonzíkFaculty of Mathematics and Physics
    Charles University
    Sokolovsk 83
    186 75 Praha 8, Czech Republic
    e-mail

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