Geodesic
Functional spaces of mixed smoothness from decompositional point of view
Informatics and Automation, Investigations in the theory of differentiable functions of many variables and its applications. Part 13, Tome 187 (1989), pp. 143-161.

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     author = {P. I. Lizorkin and S. M. Nikol'skii},
     title = {Functional spaces of mixed smoothness from decompositional point of view},
     journal = {Informatics and Automation},
     pages = {143--161},
     publisher = {mathdoc},
     volume = {187},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_1989_187_a9/}
}
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P. I. Lizorkin; S. M. Nikol'skii. Functional spaces of mixed smoothness from decompositional point of view. Informatics and Automation, Investigations in the theory of differentiable functions of many variables and its applications. Part 13, Tome 187 (1989), pp. 143-161. http://geodesic.mathdoc.fr/item/TRSPY_1989_187_a9/