  The paper is concerned with Besov spaces of variable smoothness
$B^{\varphi_{0}}_{p,q}(\mathbb{R}^{n},\{t_{k}\})$, in which the norms are
defined in terms of convolutions with smooth functions. A relation is found
between the spaces $B^{\varphi_{0}}_{p,q}(\mathbb{R}^{n},\{t_{k}\})$ and the
spaces $\widetilde{B}^{l}_{p,q,r}(\mathbb{R}^{n},\{t_{k}\})$, which were
introduced earlier by the author.
