Geodesic
Spaces of Functions of Fractional Smoothness on an Irregular Domain
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 163-183

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In this paper, we study the spaces $B_{pq}^s (G)$ and $L_{pq}^s (G)$ of functions with positive exponent of smoothness $s > 0$, defined on a domain $G\subset\mathbb R^n$. For a domain $G$ with specific geometric properties, we establish the embedding $B_{pp}^s(G)=L_{pp}^s(G)\subset L_q(G)$, $1$, with the relationship between the parameters defined by these geometric properties. 
@article{MZM_2003_74_2_a0,
     author = {O. V. Besov},
     title = {Spaces of {Functions} of {Fractional} {Smoothness} on an {Irregular} {Domain}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--183},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a0/}
}
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O. V. Besov. Spaces of Functions of Fractional Smoothness on an Irregular Domain. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 163-183. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a0/