Geodesic
Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded~$p$-Variation
Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 286-297.

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We obtain an estimate for the convergence rate of the Fourier series of a continuous periodic function in terms of the modulus of continuity of the function and the value of its $p$-variation. We prove that the leading term of the estimate is sharp.
Keywords: function of bounded $p$-variation, convergence rate of Fourier series. 
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T. Yu. Semenova. Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded~$p$-Variation. Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 286-297. http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a11/

[1] C. Jordan, “Sur la série de Fourier”, C. R. Acad. Sci. Paris, 92:5 (1881), 228–230

[2] N. Wiener, “The quadratic variation of a function and its Fourier coefficients”, J. Math. Physics, 3 (1924), 72–94 | DOI

[3] C. B. Stechkin, “Zasedaniya Moskovskogo matematicheskogo obschestva. O priblizhenii nepreryvnykh funktsii summami Fure”, UMN, 7:4 (50) (1952), 135–146

[4] C. A. Telyakovskii, “O rabotakh S. B. Stechkina po priblizheniyu periodicheskikh funktsii polinomami”, Fundament. i prikl. matem., 3:4 (1997), 1059–1068 | MR | Zbl

[5] V. V. Zhuk, Approksimatsiya periodicheskikh funktsii, Izd-vo LGU, L., 1982 | MR

[6] A. Yu. Popov, T. Yu. Semenova, “Utochnenie otsenki skorosti ravnomernoi skhodimosti ryada Fure nepreryvnoi periodicheskoi funktsii ogranichennoi variatsii”, Matem. zametki, 113:4 (2023), 544–559 | DOI | MR

[7] R. Salem, Essais sur les séries trigonométriques, Hermann Cie, Paris, 1940 | MR

[8] N. K. Bari, Trigonometricheskie ryady, GIFFL, M., 1961 | MR

[9] S. S. Volosivets, Priblizhenie funktsii ogranichennoi $p$-variatsii, Izd-vo SGU, Saratov, 2021

[10] A. P. Terekhin, “Priblizhenie funktsii ogranichennoi $p$-variatsii”, Izv. vuzov. Matem., 1965, no. 2, 171–187 | MR | Zbl

[11] L. C. Young, “An inequality of the Hölder type, connected with Stieltjes integration”, Acta Math., 67:1 (1936), 251–282 | DOI | MR

[12] V. T. Gavrilyuk, S. B. Stechkin, “Priblizhenie nepreryvnykh periodicheskikh funktsii summami Fure”, Issledovaniya po teorii funktsii mnogikh deistvitelnykh peremennykh i priblizheniyu funktsii, Tr. MIAN SSSR, 172, 1985, 107–127 | MR | Zbl

[13] G. G. Khardi, Dzh. E. Littlvud, G. Polia, Neravenstva, IL, M., 1948 | MR

[14] C. B. Stechkin, “Zamechanie k teoreme Dzheksona”, Priblizhenie funktsii v srednem, Sbornik rabot, Tr. MIAN SSSR, 88, 1967, 17–19 | MR | Zbl