Geodesic
Localization of Cesaro means of Fourier series for functions of bounded $\Lambda$-variation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2011), pp. 9-13.

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

We consider classes of periodic functions of bounded $\Lambda$-variation of the power order of growth $\Lambda$. We show that this class contains a continuous function whose Cesaro means (of a power that depends on the order of growth $\Lambda$) of the Fourier series do not satisfy the localization property.
Keywords: Cesaro means, generalized variation. 
@article{IVM_2011_8_a1,
     author = {A. N. Bakhvalov},
     title = {Localization of {Cesaro} means of {Fourier} series for functions of bounded $\Lambda$-variation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {9--13},
     publisher = {mathdoc},
     number = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_8_a1/}
}
TY  - JOUR
AU  - A. N. Bakhvalov
TI  - Localization of Cesaro means of Fourier series for functions of bounded $\Lambda$-variation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2011
SP  - 9
EP  - 13
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2011_8_a1/
LA  - ru
ID  - IVM_2011_8_a1
ER  - 
%0 Journal Article
%A A. N. Bakhvalov
%T Localization of Cesaro means of Fourier series for functions of bounded $\Lambda$-variation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2011
%P 9-13
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2011_8_a1/
%G ru
%F IVM_2011_8_a1
A. N. Bakhvalov. Localization of Cesaro means of Fourier series for functions of bounded $\Lambda$-variation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2011), pp. 9-13. http://geodesic.mathdoc.fr/item/IVM_2011_8_a1/

[1] Waterman D., “On convergence of Fourier series of functions of generalized bounded variation”, Studia math., 44:2 (1972), 107–117 | MR | Zbl

[2] Waterman D., “On the summability of Fourier series of functions of $\Lambda$-bounded variation”, Studia math., 55:1 (1976), 87–95 | MR | Zbl

[3] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965 | MR

[4] Sablin A. I., “$\Lambda$-variatsiya i ryady Fure”, Izv. vuzov. Matem., 1987, no. 10, 66–68 | MR | Zbl

[5] Perlman S., Waterman D., “Some remarks on functions of $\Lambda$-bounded variation”, Proc. Amer. Math. Soc., 74:1 (1979), 113–118 | MR | Zbl

[6] Waterman D., “On $\Lambda$-bounded variation”, Studia math., 57:1 (1976), 33–45 | MR | Zbl