Geodesic
Traces of functions with majorizable derivatives
Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 499-506.

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We study the limiting values ($y\to+0$) of functions $f(x,y)$: $x\in R_n$, $y>0$, for which $\left|{\partial f}/{\partial y}\right|\leqslant M\varphi(y)$; $\left|{\partial f}/{\partial x_k}\right|\leqslant M\psi_k(y)$, $M=M[f]$, in the case of arbitrary weight functions. It is shown that the space of traces can be described as the set of all functions $f(x,0)$ which satisfy a Lipschitz condition in some metric $\omega(x,\tilde{x})$ associated with the weights. 
@article{MZM_1975_18_4_a2,
     author = {G. A. Kalyabin},
     title = {Traces of functions with majorizable derivatives},
     journal = {Matemati\v{c}eskie zametki},
     pages = {499--506},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a2/}
}
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G. A. Kalyabin. Traces of functions with majorizable derivatives. Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 499-506. http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a2/