Geodesic
Characterization of spaces of generalized Liouville differentiation
Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 37-42 Cet article a éte moissonné depuis la source Math-Net.Ru

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The spaces mentioned in the title are described in terms of properties of integrated central differences. For the case of ordinary $L$-classes the corresponding result was obtained by P. I. Lizorkin. Bibliography: 4 titles. 
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G. A. Kalyabin. Characterization of spaces of generalized Liouville differentiation. Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 37-42. http://geodesic.mathdoc.fr/item/SM_1977_33_1_a2/

[1] S. M. Nikolskii, Priblizhenie funktsii neskolkikh peremennykh i teoremy vlozheniya, izd-vo «Nauka», Moskva, 1969 | MR

[2] L. R. Volevich, B. P. Paneyakh, “Nekotorye prostranstva obobschennykh funktsii i teoremy vlozheniya”, Uspekhi matem. nauk, XX:(121) (1965), 3–74

[3] P. I. Lizorkin, “Opisanie prostranstv $L_p^r(R_n)$ v terminakh singulyarnykh raznostnykh integralov”, Matem. sb., 81 (123) (1970), 79–91 | MR | Zbl

[4] G. A. Kalyabin, “Prostranstva sledov dlya odnogo semeistva periodicheskikh vesovykh klassov”, Trudy matem. in-ta im. V. A. Steklova, CXL, 1976, 169–180 | MR | Zbl