Geodesic
Refined theorems of approximation theory in the space of $p$-absolutely continuous functions
Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 701-711.

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In this paper, we prove direct and inverse theorems of approximation theory in the space of $p$-absolutely continuous functions which generalize Terekhin's results in the same way as Timan's results in $L_p$ generalize the classical theorems of approximation theory. The main theorems are refined for functions with quasimonotone Fourier coefficients and, in a number of cases, the resulats are shown to be sharp. 
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S. S. Volosivets. Refined theorems of approximation theory in the space of $p$-absolutely continuous functions. Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 701-711. http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a5/

[1] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960

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

[3] M. F. Timan, “Obratnye teoremy konstruktivnoi teorii funktsii v prostranstvakh $L_p$”, Matem. sb., 46:1 (1958), 125–132 | MR | Zbl

[4] M. F. Timan, “O teoreme Dzheksona v prostranstve $L_p$”, Ukr. matem. zh., 18:1 (1966), 134–137 | MR | Zbl

[5] S. S. Volosivets, “Polinomy nailuchshego priblizheniya i sootnosheniya mezhdu modulyami nepreryvnosti v prostranstvakh funktsii ogranichennoi $p$-variatsii”, Izv. vuzov. Matem., 1996, no. 9, 21–26 | MR | Zbl

[6] S. S. Volosivets, “Convergence of series of Fourier coefficients of $p$-absolutely continuous functions”, Anal. Math., 26:1 (2000), 63–80 | DOI | MR | Zbl

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

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

[9] A. P. Terekhin, “Integralnye svoistva gladkosti periodicheskikh funktsii ogranichennoi $p$-variatsii”, Matem. zametki, 2:3 (1967), 289–300 | Zbl

[10] B. I. Golubov, “O nailuchshem priblizhenii $p$-absolyutno nepreryvnykh funktsii”, Nekotorye voprosy teorii funktsii i funktsionalnogo analiza, 4, Izd-vo Tbil. un-ta, Tbilisi, 1988, 85–99

[11] G. Khardi, Dzh. Littlvud, G. Polia, Neravenstva, IL, M., 1948

[12] A. A. Konyushkov, “Nailuchshie priblizheniya trigonometricheskimi polinomami i koeffitsienty Fure”, Matem. sb., 44:1 (1958), 53–84 | Zbl

[13] V. M. Kokilashvili, “O priblizhenii periodicheskikh funktsii”, Tr. Tbil. matem. in-ta, 34 (1968), 51–81 | Zbl

[14] A. Zigmund, Trigonometricheskie ryady, t. 1, Mir, M., 1965 | MR

[15] N. A. Ilyasov, “Priblizhenie periodicheskikh funktsii srednimi Zigmunda”, Matem. zametki, 39:3 (1986), 367–382 | MR | Zbl

[16] N. K. Bari, S. B. Stechkin, “Nailuchshie priblizheniya i differentsialnye svoistva dvukh sopryazhennykh funktsii”, Tr. MMO, 5, 1956, 483–522 | MR | Zbl

[17] S. S. Volosivets, “Asimptoticheskie kharakteristiki odnogo kompakta gladkikh funktsii v prostranstve funktsii ogranichennoi $p$-variatsii”, Matem. zametki, 57:2 (1995), 214–227 | MR | Zbl