Geodesic
A multidimensional analogue of a~theorem of F.~Riesz
Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1363-1374

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In this paper a multidimensional analogue of a theorem of F. Riesz is proved which deals with conditions for the representability of a given function as the indefinite integral of a function of bounded variation. Our result is formulated via the notion of Vitali essential variation of functions of several variables, which was introduced in an earlier paper by the author. 
@article{SM_1995_186_9_a8,
     author = {F. A. Talalian},
     title = {A multidimensional analogue of a~theorem of {F.~Riesz}},
     journal = {Sbornik. Mathematics},
     pages = {1363--1374},
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     volume = {186},
     number = {9},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_9_a8/}
}
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F. A. Talalian. A multidimensional analogue of a~theorem of F.~Riesz. Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1363-1374. http://geodesic.mathdoc.fr/item/SM_1995_186_9_a8/