Geodesic
A Discrete Norm on a~Lipschitz Surface and the~Sobolev Straightening of a~Boundary
Matematičeskie trudy, Tome 10 (2007) no. 2, pp. 163-186

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Let a piece of the boundary of a Lipschitz domain be parameterized conventionally and let the traces of functions in the Sobolev space $W^2_p$ be written out through this parameter. In this space, we propose a discrete (diadic) norm generalizing A. Kamont's norm in the plane case. We study the conditions when the space of traces coincides with the corresponding space for the plane boundary. 
@article{MT_2007_10_2_a6,
     author = {A. I. Parfenov},
     title = {A {Discrete} {Norm} on {a~Lipschitz} {Surface} and {the~Sobolev} {Straightening} of {a~Boundary}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {163--186},
     publisher = {mathdoc},
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A. I. Parfenov. A Discrete Norm on a~Lipschitz Surface and the~Sobolev Straightening of a~Boundary. Matematičeskie trudy, Tome 10 (2007) no. 2, pp. 163-186. http://geodesic.mathdoc.fr/item/MT_2007_10_2_a6/