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The abstract of the following paper sounds like it might be relevant to your first question. Unfortunately, I do not have access to the journal: D. Kim, Trace theorems for Sobolev-Slobedeckij spaces with our or without weights, Journal of Function Spaces and Applications 5 (2007), 243-268.

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The abstract of the following paper sounds like it might be relevant to your first question. Unfortunately, I do not have access to the journal: D. Kim, Trace theorems for Sobolev-Slobedeckij spaces with our without weights, Journal of Function Spaces and Applications 5 (2007), 243-268.