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 $\mathbb R^n$.