Geodesic
Divergence everywhere of subsequences of partial sums of trigonometric Fourier series
Trudy Instituta matematiki i mehaniki, Function theory, Tome 11 (2005) no. 2, pp. 112-119 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

It is proved that for any increasing sequence of natural numbers $\{m_j\}$ and any nondecreasing function $\varphi\colon[0,+\infty)\to[0,+\infty)$ satisfying the condition $\varphi(u)=o(u\ln\ln)$ ($u\to\infty$) there is a function $f\in L[0,2\pi]$ such that $$ \int_0^{2\pi}\varphi(|f(x)|)\,dx\infty, $$ and the Fourier partial sums $S_{m_j}(f)$ diverge unboundedly everywhere. 
@article{TIMM_2005_11_2_a8,
     author = {S. V. Konyagin},
     title = {Divergence everywhere of subsequences of partial sums of trigonometric {Fourier} series},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {112--119},
     year = {2005},
     volume = {11},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2005_11_2_a8/}
}
TY  - JOUR
AU  - S. V. Konyagin
TI  - Divergence everywhere of subsequences of partial sums of trigonometric Fourier series
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2005
SP  - 112
EP  - 119
VL  - 11
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2005_11_2_a8/
LA  - ru
ID  - TIMM_2005_11_2_a8
ER  - 
%0 Journal Article
%A S. V. Konyagin
%T Divergence everywhere of subsequences of partial sums of trigonometric Fourier series
%J Trudy Instituta matematiki i mehaniki
%D 2005
%P 112-119
%V 11
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2005_11_2_a8/
%G ru
%F TIMM_2005_11_2_a8
S. V. Konyagin. Divergence everywhere of subsequences of partial sums of trigonometric Fourier series. Trudy Instituta matematiki i mehaniki, Function theory, Tome 11 (2005) no. 2, pp. 112-119. http://geodesic.mathdoc.fr/item/TIMM_2005_11_2_a8/

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

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

[3] Sjölin P., “An inequality of Paley and convergence a.e. of Walsh–Fourier series”, Ark. Mat., 7 (1969), 551–570 | DOI | MR | Zbl

[4] Kolmogoroff A. N., “Une série de Fourier–Lebesgue divergente presque partout”, Fund. Math., 4 (1923), 324–328 | Zbl

[5] Kolmogoroff A. N., “Une série de Fourier–Lebesgue divergente partout”, C. R. Acad. Sci. Paris, 183 (1926), 1327–1329

[6] Bari N. K., Trigonometricheskie ryady, GIFML, M., 1961 | MR

[7] Körner T. W., “Everywhere divergent Fourier series”, Colloq. Math., 45 (1981), 103–118 | MR | Zbl

[8] Konyagin S. V., “O raskhodimosti vsyudu trigonometricheskikh ryadov Fure”, Matem. sb., 191:1 (2000), 103–126 | MR | Zbl

[9] Zigmund A., Trigonometricheskie ryady, T. 1,2, Mir, M., 1965 | MR

[10] Totik V., “On the divergence of Fourier series”, Publ. Math. (Debrecen), 29 (1982), 251–264 | MR | Zbl

[11] Kheladze Sh. V., “O raskhodimosti vsyudu ryadov Fure funktsii iz klassa $L_\varphi(L)$”, Tr. Tbil. mat. in-ta, 89, 1988, 51–59 | MR

[12] Krasnoselskii M. A., Rutitskii Ya. B., Vypuklye funktsii i prostranstva Orlicha, GIFML, M., 1958