A~mixed $q$-integral $p$-variation, and theorems of equivalence and imbedding of classes of functions with a~mixed modulus of smoothness
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Investigations in the theory of differentiable functions of many variables and its applications. Part 7, Tome 150 (1979), pp. 306-319.

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     author = {A. P. Terekhin},
     title = {A~mixed $q$-integral $p$-variation, and theorems of equivalence and imbedding of classes of functions with a~mixed modulus of smoothness},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {306--319},
     publisher = {mathdoc},
     volume = {150},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1979_150_a15/}
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A. P. Terekhin. A~mixed $q$-integral $p$-variation, and theorems of equivalence and imbedding of classes of functions with a~mixed modulus of smoothness. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Investigations in the theory of differentiable functions of many variables and its applications. Part 7, Tome 150 (1979), pp. 306-319. http://geodesic.mathdoc.fr/item/TM_1979_150_a15/