On Embedding of Besov Spaces of Zero Smoothness into Lorentz Spaces

We show that the zero smoothness Besov space $B_{p,q}^{0,1}$ does not embed into the Lorentz space $L_{p,q}$ unless $p=q$; here $p,q\in (1,\infty )$. This answers in the negative a question posed by O. V. Besov.