On spaces of functions of smoothness zero

The paper is concerned with the new spaces $\overline B{}_{p,q}^0$ of functions of smoothness zero defined on the $n$-dimensional Euclidean space $\mathbb R^n$ or on a subdomain $G$ of $\mathbb R^n$. These spaces are compared with the spaces $B_{p,q}^0(\mathbb R^n)$ and $\mathrm{bmo}(\mathbb R^n)$. The embedding theorems for Sobolev spaces are refined in terms of the space $\overline B{}_{p,q}^0$ with the limiting exponent.
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