On the divergence of triangular and eccentric spherical sums of double Fourier series
Sbornik. Mathematics, Tome 207 (2016) no. 1, pp. 65-84 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We construct a continuous function on the torus with almost everywhere divergent triangular sums of double Fourier series. We also prove an analogous theorem for eccentric spherical sums. Bibliography: 14 titles.
Keywords: divergent triangular sums, double Fourier series.
@article{SM_2016_207_1_a2,
     author = {G. A. Karagulyan},
     title = {On the divergence of triangular and eccentric spherical sums of double {Fourier} series},
     journal = {Sbornik. Mathematics},
     pages = {65--84},
     year = {2016},
     volume = {207},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_1_a2/}
}
TY  - JOUR
AU  - G. A. Karagulyan
TI  - On the divergence of triangular and eccentric spherical sums of double Fourier series
JO  - Sbornik. Mathematics
PY  - 2016
SP  - 65
EP  - 84
VL  - 207
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_2016_207_1_a2/
LA  - en
ID  - SM_2016_207_1_a2
ER  - 
%0 Journal Article
%A G. A. Karagulyan
%T On the divergence of triangular and eccentric spherical sums of double Fourier series
%J Sbornik. Mathematics
%D 2016
%P 65-84
%V 207
%N 1
%U http://geodesic.mathdoc.fr/item/SM_2016_207_1_a2/
%G en
%F SM_2016_207_1_a2
G. A. Karagulyan. On the divergence of triangular and eccentric spherical sums of double Fourier series. Sbornik. Mathematics, Tome 207 (2016) no. 1, pp. 65-84. http://geodesic.mathdoc.fr/item/SM_2016_207_1_a2/

[1] L. Carleson, “On convergence and growth of partial sums of Fourier series”, Acta Math., 116 (1966), 135–157 | DOI | MR | Zbl

[2] R. A. Hunt, “On the convergence of Fourier series”, Orthogonal expansions and their continuous analogues (Edwardsville, Ill., 1967), Southern Illinois Univ. Press, Carbondale, Ill., 1968, 235–255 | MR | Zbl

[3] P. Sjölin, “Convergence almost everywhere of certain singular integrals and multiple Fourier series”, Ark. Mat., 9 (1971), 65–90 | DOI | MR | Zbl

[4] N. Yu. Antonov, “Convergence of Fourier series”, East J. Approx., 2:2 (1996), 187–196 | MR | Zbl

[5] C. Fefferman, “On the convergence of multiple Fourier series”, Bull. Amer. Math. Soc., 77:5 (1971), 744–745 | DOI | MR | Zbl

[6] N. R. Tevzadze, “O skhodimosti dvoinogo ryada Fure funktsii, summiruemoi s kvadratom”, Soobsch. AN Gruz. SSR, 58:2 (1970), 277–279 | MR | Zbl

[7] C. Fefferman, “On the divergence of multiple Fourier series”, Bull. Amer. Math. Soc., 77:2 (1971), 191–195 | DOI | MR | Zbl

[8] G. A. Karagulyan, K. R. Muradyan, “Divergent triangular sums of double Fourier series”, J. Contemp. Math. Anal., 50:4 (2015), 196–207 | DOI

[9] G. A. Karagulyan, K. R. Muradyan, “On the divergence of Walsh and Haar series by sectorial and triangular regions”, Proc. Yerevan State Univ. Phys. Math. Sci., 234:2 (2014), 3–12 | Zbl

[10] G. A. Karagulyan, “On unboundedness of maximal operators for directional Hilbert transforms”, Proc. Amer. Math. Soc., 135:10 (2007), 3133–3141 | DOI | MR | Zbl

[11] A. Zygmund, Trigonometric series, v. I, 2nd ed., Cambridge Univ. Press, New York, 1959, xii+383 pp. | MR | MR | Zbl | Zbl

[12] E. M. Nikishin, P. L. Ulyanov, “Ob absolyutnoi i bezuslovnoi skhodimosti”, UMN, 22:3(135) (1967), 240–242 | MR

[13] B. S. Kashin, A. A. Saakyan, Orthogonal series, Transl. Math. Monogr., 75, Amer. Math. Soc., Providence, RI, 1989, xii+451 pp. | MR | MR | Zbl | Zbl

[14] J. Neveu, Bases mathématiques du calcul des probabilités, Masson et Cie, Éditeurs, Paris, 1964, xiii+203 pp. | MR | MR | Zbl | Zbl