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 _p ² 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.