Geodesic
Traces of differentiable functions on subsets of Euclidean space
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 52-66

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We investigate conditions of existence and coincideness of the traces of functions of Sobolev's and Besov's classes both in the operator sense and in the sense of strict definiteness. A solution is given to the problems on trace and extension for the trace operator $\operatorname{Tr}\colon B\to L^p$ in the case, when $\Gamma$ is a countably $(\mathcal H_m,m)$ – rectifiable $\mathcal H$-measurable subset of $\mathbb R^n$. 
@article{ZNSL_1986_149_a3,
     author = {A. B. Gulisashvili},
     title = {Traces of differentiable functions on subsets of {Euclidean} space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {52--66},
     publisher = {mathdoc},
     volume = {149},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a3/}
}
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A. B. Gulisashvili. Traces of differentiable functions on subsets of Euclidean space. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 52-66. http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a3/