Geodesic
The weighted spaces $L^\alpha_{p,r}(\rho_1,\rho_2)$ of differentiable functions of fractional smoothness
Sbornik. Mathematics, Tome 59 (1988) no. 1, pp. 209-221

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This is an investigation of weighted spaces of differentiable functions of fractional smoothness consisting of functions $f(x)$ which are $r$-integrable with a weight $\rho_1$ and have “fractional derivatives” which are p-integrable with a weight $\rho_2$. Bibliography: 20 titles. 
@article{SM_1988_59_1_a10,
     author = {V. A. Nogin},
     title = {The weighted spaces $L^\alpha_{p,r}(\rho_1,\rho_2)$ of differentiable functions of fractional smoothness},
     journal = {Sbornik. Mathematics},
     pages = {209--221},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_59_1_a10/}
}
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V. A. Nogin. The weighted spaces $L^\alpha_{p,r}(\rho_1,\rho_2)$ of differentiable functions of fractional smoothness. Sbornik. Mathematics, Tome 59 (1988) no. 1, pp. 209-221. http://geodesic.mathdoc.fr/item/SM_1988_59_1_a10/