Geodesic
On sets of absolute convergence
Sbornik. Mathematics, Tome 38 (1981) no. 2, pp. 245-254 
R. A. Avetisyan. On sets of absolute convergence. Sbornik. Mathematics, Tome 38 (1981) no. 2, pp. 245-254. http://geodesic.mathdoc.fr/item/SM_1981_38_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the author indicates a certain class of planar curves such that any set of positive linear measure on them is a set of absolute convergence for double trigonometric series. Bibliography: 11 titles.

[1] S. B. Stechkin, P. L. Ulyanov, Podposledovatelnosti skhodimosti ryadov, Trudy Matem. in-ta im. V. A. Steklova, LXXXVI, 1965 | MR

[2] G. Reva and Szàsz, “Some theorems on double trigonometric series”, Duke Math. J., 9 (1942), 693–705 | DOI | MR

[3] H. H. Luzin, “Sur l'absolue convergence des séries trigonométriques”, C. r. Acad. scient., 155 (1912), 580–582

[4] A. Denjoy, “Sur l'absolue convergence des séries trigonométriques”, C. r. Acad. scient., 155 (1912), 135–136 | Zbl

[5] P. A. Avetisyan, “O $D$-svoistve funktsionalnykh posledovatelnostei”, Izv. AN Arm. SSR, Matematika, XI:3 (1976), 222–228

[6] R. A. Avetisyan, “O mnozhestvakh absolyutnoi skhodimosti dvoinykh trigonometricheskikh ryadov”, Matem. zametki, 11:5 (1972), 473–480 | Zbl

[7] R. A. Avetisyan, “O mnozhestvakh absolyutnoi skhodimosti kratnykh trigonometricheskikh ryadov”, Matem. zametki, 13:5 (1973), 625–635

[8] V. V. Nemytskii, “O nekotorykh klassakh lineinykh mnozhestv v svyazi s absolyutnoi skhodimostyu trigonometricheskikh ryadov”, Matem. sb., 33 (1926), 5–32 | Zbl

[9] M. Ash and Velland, “Convergence, uniqueness and summability of multiple trigonometric series”, Trans. Amer. Math. Soc., 163 (1972), 401–445 | DOI | MR

[10] A. Zigmund, Trigonometricheskie ryady, t. 1, izd-vo “Mir”, Moskva, 1965 | MR

[11] N. K. Bari, Trigonometricheskie ryady, Fizmatgiz, Moskva, 1961 | MR