  It is known that the Sobolev space $L^2_s$ with $s>n/2$ appeared in the
H\"ormander multiplier theorem can be replaced by the Besov space
$B^{2,1}_{n/2}$. On the other hand, the Besov space $B_{n/2}^{2,1}$ is
continuously embedded in the modulation space $M^{2,1}_0$. In this paper, we
consider the problem whether we can replace $B_{n/2}^{2,1}$ by $M^{2,1}_0$.
