Geodesic
Function Spaces of Lizorkin--Triebel Type on an Irregular Domain
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 32-43

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On an irregular domain $G\subset\mathbb R^n$ of a certain type, we introduce function spaces of fractional smoothness $s>0$ that are similar to the Lizorkin–Triebel spaces. We prove embedding theorems that show how these spaces are related to the Sobolev and Lebesgue spaces $W_p^m(G)$ and $L_p(G)$. 
@article{TM_2008_260_a2,
     author = {O. V. Besov},
     title = {Function {Spaces} of {Lizorkin--Triebel} {Type} on an {Irregular} {Domain}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {32--43},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_260_a2/}
}
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O. V. Besov. Function Spaces of Lizorkin--Triebel Type on an Irregular Domain. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 32-43. http://geodesic.mathdoc.fr/item/TM_2008_260_a2/