Geodesic
The Problem of Traces for Sobolev Spaces with Muckenhoupt-Type Weights
Matematičeskie zametki, Tome 94 (2013) no. 5, pp. 720-732.

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An exact description of traces of functions from the weighted Sobolev space $W_{p}^{l}(Q,\gamma)$ on the square are presented in detail. The weight function $\gamma \in A_p((0,1))$ depends on one “longitudinal” coordinate $x$. Traces are characterized in terms of the weighted Besov-type spaces $\widetilde{B}_{p}^{l-1/p}((0,1),\gamma)$ constructed in the paper. The characterization of traces is also obtained in the case $p=1$.
Keywords: trace of a function, weighted Sobolev space $W_{p}^{l}(Q,\gamma)$, weighted Besov-type spaces, Muckenhoupt-type weight, Hölder's inequality, Minkowski's inequality. 
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A. I. Tjulenev. The Problem of Traces for Sobolev Spaces with Muckenhoupt-Type Weights. Matematičeskie zametki, Tome 94 (2013) no. 5, pp. 720-732. http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a7/

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