An exponential estimate for the cubic partial sums of multiple Fourier series
Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 273-286.

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

We prove an exponential integral estimate for the cubic partial sums of multiple Fourier series on sets of large measure. This estimate yields some new properties of Fourier series.
Keywords: multiple Fourier series, exponential integral estimates, cubic partial sums.
@article{IM2_2019_83_2_a5,
     author = {G. A. Karagulyan and H. Mkoyan},
     title = {An exponential estimate for the cubic partial sums of multiple {Fourier} series},
     journal = {Izvestiya. Mathematics },
     pages = {273--286},
     publisher = {mathdoc},
     volume = {83},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a5/}
}
TY  - JOUR
AU  - G. A. Karagulyan
AU  - H. Mkoyan
TI  - An exponential estimate for the cubic partial sums of multiple Fourier series
JO  - Izvestiya. Mathematics 
PY  - 2019
SP  - 273
EP  - 286
VL  - 83
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a5/
LA  - en
ID  - IM2_2019_83_2_a5
ER  - 
%0 Journal Article
%A G. A. Karagulyan
%A H. Mkoyan
%T An exponential estimate for the cubic partial sums of multiple Fourier series
%J Izvestiya. Mathematics 
%D 2019
%P 273-286
%V 83
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a5/
%G en
%F IM2_2019_83_2_a5
G. A. Karagulyan; H. Mkoyan. An exponential estimate for the cubic partial sums of multiple Fourier series. Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 273-286. http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a5/

[1] A. Zygmund, “On the convergence and summability of power series on the circle of convergence. II”, Proc. London Math. Soc. (2), 47 (1942), 326–350 | DOI | MR | Zbl

[2] L. V. Žižiašvili, “A generalization of a theorem of Marcinkiewicz”, Math. USSR-Izv., 2:5 (1968), 1065–1075 | DOI | MR | Zbl

[3] S. V. Konyagin, “On the divergence of a subsequence of the partial sums of multiple trigonometric Fourier series”, Proc. Steklov Inst. Math., 190 (1992), 107–121 | MR | Zbl

[4] R. D. Getsadze, “O raskhodimosti po mere kratnykh ryadov Fure”, Soobsch. AN Gruz. SSR, 122:2 (1986), 269–271 | MR | Zbl

[5] S. A. Nazarov, “Two-term asymptotics of solutions of spectral problems with singular perturbations”, Math. USSR-Sb., 69:2 (1991), 307–340 | DOI | MR | Zbl

[6] G. A. Karagulian, “Exponential estimates of the Calderón–Zygmund operator and related questions about Fourier series”, Math. Notes, 71:3 (2002), 362–373 | DOI | DOI | MR | Zbl

[7] K. I. Oskolkov, “Subsequences of Fourier sums of integrable functions”, Proc. Steklov Inst. Math., 167 (1986), 267–290 | MR | Zbl

[8] G. A. Karagulyan, “Exponential estimates for partial sums of Fourier series in the Walsh system and the rearranged Haar system”, J. Contemp. Math. Anal., 36:5 (2001), 19–30 | MR

[9] G. A. Karagulyan, “On $L^p$ convergence of orthogonal series on the sets of nearly full measure”, J. Contemp. Math. Anal., 29:2 (1994), 50–56 | MR | Zbl

[10] M. I. D'yachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171 | DOI | MR | Zbl

[11] P. Sjölin, “Convergence almost everywhere of certain singular integrals and multiple Fourier series”, Ark. Mat., 9:1-2 (1971), 65–90 | DOI | MR | Zbl

[12] M. A. Krasnosel'skii, Ya. B. Rutickii, Convex functions and Orlicz spaces, P. Noordhoff Ltd., Groningen, 1961, xi+249 pp. | MR | MR | Zbl | Zbl

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

[14] U. Goginava, L. Gogoladze, G. Karagulyan, “BMO-estimation and almost everywhere exponential summability of quadratic partial sums of double Fourier series”, Constr. Approx., 40:1 (2014), 105–120 | DOI | MR | Zbl