A Discrete Norm on a Lipschitz Surface and the Sobolev Straightening of a Boundary

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.