Geodesic
A multidimensional analogue of a theorem of F. Riesz
Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1363-1374 
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/
@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},
     year = {1995},
     volume = {186},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_9_a8/}
}
TY  - JOUR
AU  - F. A. Talalian
TI  - A multidimensional analogue of a theorem of F. Riesz
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 1363
EP  - 1374
VL  - 186
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_1995_186_9_a8/
LA  - en
ID  - SM_1995_186_9_a8
ER  - 
%0 Journal Article
%A F. A. Talalian
%T A multidimensional analogue of a theorem of F. Riesz
%J Sbornik. Mathematics
%D 1995
%P 1363-1374
%V 186
%N 9
%U http://geodesic.mathdoc.fr/item/SM_1995_186_9_a8/
%G en
%F SM_1995_186_9_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Riesz F., “Untersuchungen uber systeme intergrierbarer Funktionen”, Math. Ann., 69 (1910), 449–497 ; Oeuvres completes, T. 1, Budapest, 1960, 441–489 | DOI | MR | Zbl

[2] Riesz F., “Sur certains systems singuliers d'equations integrales”, Ann. Eq. Norm., 28:3 (1911), 36–65 ; Oeuvres completes, T. 2, Budapest, 1960, 798–827 | MR

[3] Medvedev Yu. T., “Obobschenie odnoi teoremy F. Rissa”, UMN, 8:6 (58) (1953), 115–118 | MR | Zbl

[4] Kudryavtsev L. D., “O $p$-variatsii otobrazhenii i summiruemosti stepenei proizvodnoi Radona–Nikodima”, UMN, 10:2 (1955), 167–174 | MR

[5] Fuglede B., “On a theorem of F. Riesz”, Math. Scand., 3 (1955), 283–302 | MR | Zbl

[6] Talalyan F. A., “O suschestvennoi variatsii v smysle Vitali funktsii mnogikh peremennykh”, Izv. AN Armenii. Matematika, 28:4 (1993) | MR

[7] Talalyan F. A., “Monotonnye funktsii mnogikh peremennykh i mnogomernaya vtoraya teorema o srednem”, Izv. AN Armenii. Matematika, 27:2 (1992), 83–103 | MR

[8] Charatheodory C., Vorlesungen uber reele funktionen, Leipzig–Berlin, 1927