A sharp version of the Hörmander multiplier theorem

Abstract

We provide an improvement of the Hörmander multiplier theorem in which the Sobolev space $L_s^r({\mathbb{R}}^n)$ with integrability index $r$ and smoothness index $s>n/r$ is replaced by the Sobolev space with smoothness $s$ built upon the Lorentz space $L^{n/s,1}({\mathbb{R}}^n)$.