Multipliers on Besov spaces

It is proved that the characteristic function of a halfepace $\mathbb R_n^+$ is not a multiplier for the pair $(B_{pq}^{1/p}, B_{p\infty}^{1/p})$, $1<p<\infty$, $1<q\leqslant\infty$. A necessary and sufficient condition is given for $\chi_E$ to belong to $\in M(B_{p1}^{1/p}\to B_{p\infty}^{1/p})$.