Geodesic
On a~convergence in $L_p$ of the Cesaro means оf Fourier series with monotonic coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2016), pp. 24-30.

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

In this paper we study a convergence in $L_p$, $1$, of the Cesaro means of negative order for sine and cosine Fourier series with monotonic coefficients.
Keywords: Cesaro means, integral modulus of continuity, Fourier series with monotonic coefficients, summability in $L_p$ space. 
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L. N. Galoyan. On a~convergence in $L_p$ of the Cesaro means оf Fourier series with monotonic coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2016), pp. 24-30. http://geodesic.mathdoc.fr/item/IVM_2016_2_a3/

[1] Taberski R., “On the convergence of singular integrals”, Zesyty Naukowe Uniw. A. Mickewicza. Math. Fiz. Chem., 2 (1960), 33–51 | MR | Zbl

[2] Ulyanov P. L., “O priblizhenii funktsii”, Sib. matem. zhurn., 5:2 (1964), 418–437 | Zbl

[3] Menshov D. E., “Primenenie metodov summirovaniya Chezaro otritsatelnogo poryadka k trigonometricheskim ryadam Fure ot summiruemykh funktsii i ot funktsii s summiruemym kvadratom”, Matem. sb., 93(135):4 (1974), 494–511 | MR | Zbl

[4] Kudryavtsev A. I., Survillo G. S., “Ob odnom kriterii $L_p$ summiruemosti ryadov Fure metodami Chezaro otritsatelnogo poryadka”, Izv. vuzov. Matem., 1990, no. 11, 47–50 | MR | Zbl

[5] Zhizhiashvili L. V., “O skhodimosti i summiruemosti trigonometricheskikh ryadov Fure”, Matem. zametki, 19:6 (1976), 887–898 | MR | Zbl

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

[7] Galoyan L. N., “O skhodimosti v metrikakh $L_p$, $p>1$, srednikh Chezaro otritsatelnogo poryadka ryadov Fure–Uolsha”, Izv. NAN Armenii, 47:6 (2012), 25–40 | MR

[8] Zygmund A., Trigonometric series, v. 1, Cambrige, 1959

[9] Khardi G., Raskhodyaschiesya ryady, In lit., M., 1951

[10] Golubov B. I., Efimov A. F., Skvortsov V. A., Ryady i preobrazovaniya Uolsha, Nauka, M., 1987 | MR

[11] Dyachenko M. I., “Teorema Khardi–Littlvuda dlya trigonometricheskikh ryadov s obobschenno monotonnymi koeffitsientami”, Izv. vuzov. Matem., 2008, no. 5, 38–47 | MR | Zbl