Geodesic
On the mean convergence of multiple Fourier series and the asymptotics of the Dirichlet kernel of spherical means
Eurasian mathematical journal, Tome 9 (2018) no. 4, pp. 22-60 
K. I. Babenko. On the mean convergence of multiple Fourier series and the asymptotics of the Dirichlet kernel of spherical means. Eurasian mathematical journal, Tome 9 (2018) no. 4, pp. 22-60. http://geodesic.mathdoc.fr/item/EMJ_2018_9_4_a2/
@article{EMJ_2018_9_4_a2,
     author = {K. I. Babenko},
     title = {On the mean convergence of multiple {Fourier} series and the asymptotics of the {Dirichlet} kernel of spherical means},
     journal = {Eurasian mathematical journal},
     pages = {22--60},
     year = {2018},
     volume = {9},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2018_9_4_a2/}
}
TY  - JOUR
AU  - K. I. Babenko
TI  - On the mean convergence of multiple Fourier series and the asymptotics of the Dirichlet kernel of spherical means
JO  - Eurasian mathematical journal
PY  - 2018
SP  - 22
EP  - 60
VL  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/EMJ_2018_9_4_a2/
LA  - en
ID  - EMJ_2018_9_4_a2
ER  - 
%0 Journal Article
%A K. I. Babenko
%T On the mean convergence of multiple Fourier series and the asymptotics of the Dirichlet kernel of spherical means
%J Eurasian mathematical journal
%D 2018
%P 22-60
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/EMJ_2018_9_4_a2/
%G en
%F EMJ_2018_9_4_a2

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

Preprint no. 52 (1971), Institut Prikladnoi Matematiki Akademii Nauk USSR, Moscow (in Russian). Translated into English by E. Liflyand. See comments to this paper by E. Liflyand in this volume of the Eurasian Mathematical Journal.

[1] A. Beurling, “Ensembles exceptionnels”, Acta Math., 72 (1940), 1–13 | DOI

[2] G. Hardy, E. Landau, “The lattice points of a circle”, Proc. Royal Soc. (A), 1925, 224–258

[3] Russian Math. Surveys, 23 (1968), 59–116 | DOI

[4] A. N. Kolmogorov, “Une série de Fourier-Lebesgue divergente partout”, C.R. Acad. Sci. Paris, Ser. I, 183 (1926), 1327–1328

[5] B. M. Levitan, “On summability of multiple series and Fourier integrals”, Dokl. Akad. Nauk SSSR (N.S.), 102 (1955), 1073–1076 (in Russian)

[6] A. Oppenheim, “Some identities in the theory of numbers”, Proc. London Math. Soc. (2), 26 (1927), 295–350 | DOI

[7] R. Salem, A. Zygmund, “Capacity of sets and Fourier series”, Trans. Amer. Math. Soc., 59 (1946), 23–41 | DOI

[8] Translations of Mathematical Monographs, 7, American Mathematical Society, Providence, R.I., 1963 | DOI

[9] E. Stein, “Localization and summability of multiple Fourier series”, Acta Math., 100:1–2 (1958), 93–147 | DOI

[10] IL, M., 1953

[11] Wolters-Noordhoff Publishing, Groningen, 1970

[12] Dover Publications, Inc., New York, 1954

[13] A. Walflsz, “Uber zwei Gitterpunktprobleme”, Math. Annalen, 95 (1926), 69–83 | DOI

[14] A. Walflsz (Val'flsh), “On the representation of numbers by sums of squares. Asymptotic formulas”, Uspekhi Matem. Nauk, 7 (1952), 97–178 (in Russian)