Geodesic
Characterization of spaces of generalized Liouville differentiation
Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 37-42

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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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     author = {G. A. Kalyabin},
     title = {Characterization of spaces of generalized {Liouville} differentiation},
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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/