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. 
@article{MZM_2013_94_5_a7,
     author = {A. I. Tjulenev},
     title = {The {Problem} of {Traces} for {Sobolev} {Spaces} with {Muckenhoupt-Type} {Weights}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {720--732},
     publisher = {mathdoc},
     volume = {94},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a7/}
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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/