Geodesic
Interpolation, Embedding, and Extension of Spaces of Functions of Variable Smoothness
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 52-63

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Interpolation, embedding, and extension theorems are proved for Banach spaces $B_{p,q}^s(G)$ and $L_{p,q}^s(G)=F_{p,q}^s(G)$, $1 p,q\infty$, of functions that have a variable smoothness $s=s(x)$ and are defined on a domain $G\subset \mathbb R ^n$ with a Lipschitz boundary. 
@article{TM_2005_248_a5,
     author = {O. V. Besov},
     title = {Interpolation, {Embedding,} and {Extension} of {Spaces} of {Functions} of {Variable} {Smoothness}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {52--63},
     publisher = {mathdoc},
     volume = {248},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2005_248_a5/}
}
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O. V. Besov. Interpolation, Embedding, and Extension of Spaces of Functions of Variable Smoothness. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 52-63. http://geodesic.mathdoc.fr/item/TM_2005_248_a5/