A Sharp Version of the Hörmander Multiplier Theorem

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