Geodesic
On spaces of functions of smoothness zero
Sbornik. Mathematics, Tome 203 (2012) no. 8, pp. 1077-1090

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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. Bibliography: 8 titles.
Keywords: spaces of differentiable functions, embedding theorems
Mots-clés : Sobolev spaces. 
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     author = {O. V. Besov},
     title = {On spaces of functions of smoothness zero},
     journal = {Sbornik. Mathematics},
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     number = {8},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_8_a0/}
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O. V. Besov. On spaces of functions of smoothness zero. Sbornik. Mathematics, Tome 203 (2012) no. 8, pp. 1077-1090. http://geodesic.mathdoc.fr/item/SM_2012_203_8_a0/