Geodesic
Functions of bounded $q$-integral $p$-variation and imbedding theorems
Sbornik. Mathematics, Tome 17 (1972) no. 2, pp. 279-288

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For a function of one real variable there is defined a notion of $q$-integral $p$-variation generalizing Wiener $p$-variation. In terms of this notion there is given a necessary and sufficient condition that a function in $L_q$ have a higher derivative in $L_p$ ($p\leqslant q$), and also that the derivative have a definite smoothness in $L_p$. In addition, embedding theorems with inversion are proved in the periodic case for generalized Lipschitz classes in $L_p$. Bibliography: 9 titles. 
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     author = {A. P. Terekhin},
     title = {Functions of bounded $q$-integral $p$-variation and imbedding theorems},
     journal = {Sbornik. Mathematics},
     pages = {279--288},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_17_2_a8/}
}
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A. P. Terekhin. Functions of bounded $q$-integral $p$-variation and imbedding theorems. Sbornik. Mathematics, Tome 17 (1972) no. 2, pp. 279-288. http://geodesic.mathdoc.fr/item/SM_1972_17_2_a8/