Geodesic
Analysis of a theorem on the Jackson-Stechkin inequality in the Bergman space $B_2$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 217-224
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We present a refinement of a theorem of V.A. Abilov, F.V. Abilova, and M.K. Kerimov on the exact constant in a Jackson type inequality between the mean-square approximation of a function of a complex variable by Fourier series in a system orthogonal in a bounded domain and the generalized modulus of continuity of order $m\geq 1$.
Keywords: generalized modulus of continuity, generalized translation operator, orthonormal system, Jackson-Stechkin inequality. 
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M. S. Saidusajnov. Analysis of a theorem on the Jackson-Stechkin inequality in the Bergman space $B_2$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 217-224. http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a17/

[1] Korneichuk N.P., “Tochnaya konstanta v teoreme D. Dzheksona o nailuchshem priblizhenii nepreryvnykh periodicheskikh funktsii”, Dokl. AN, 145:3 (1962), 514–515 | Zbl

[2] Chernykh N.I., “O neravenstvakh Dzheksona v $L_2$”, Tr. MIAN, 88, 1967, 71–74

[3] Chernykh N.I., “O nailuchshem priblizhenii periodicheskikh funktsii trigonometricheskimi polinomami v $L_2$”, Mat. zametki, 2:5 (1967), 513–522

[4] Zhuk V.V., “O nekotorykh tochnykh neravenstvakh mezhdu nailuchshimi priblizheniyami i modulyami nepreryvnosti”, Dokl. AN SSSR, 196:4 (1971), 748–750 | Zbl

[5] Taikov L.V., “Neravenstva, soderzhaschie nailuchshie priblizheniya i modul nepreryvnosti iz $L_2$”, Mat. zametki, 20:3 (1976), 433–438 | MR | Zbl

[6] Ligun A.A., “Tochnye neravenstva mezhdu nailuchshimi priblizheniyami i modulyami nepreryvnosti v prostranstve $L_2$”, Mat. zametki, 24:6 (1978), 785–792 | MR | Zbl

[7] Babenko A.G., “O tochnoi konstante v neravenstve Dzheksona v $L^2$”, Mat. zametki, 39:5 (1986), 651–664 | MR | Zbl

[8] Ivanov V.I, Smirnov O.I., Konstanty Dzheksona i konstanty Yunga v prostranstve $L_p$, Izd-vo Tulskogo un-ta, Tula, 1995, 192 pp.

[9] Shabozov M.Sh., Yusupov G.A., “Nailuchshie polinomialnye priblizheniya v $L_2$ nekotorykh klassov $2\pi$-periodicheskikh funktsii i tochnye znacheniya ikh poperechnikov”, Mat. zametki, 90:5 (2011), 764–775 | DOI | MR | Zbl

[10] Vakarchuk S.B., Zabutnaya V.I., “Neravenstva tipa Dzheksona - Stechkina dlya spetsialnykh modulei nepreryvnosti i poperechniki funktsionalnykh klassov v prostranstve $L_2$”, Mat. zametki, 92:4 (2012), 497–514 | DOI | Zbl

[11] Smirnov V.I., Lebedev N.A., Konstruktivnaya teoriya funktsii kompleksnogo peremennogo, Nauka, M.; L., 1964, 440 pp.

[12] Abilov V.A., Abilova F.V., Kerimov M.K., “Tochnye otsenki skorosti skhodimosti ryadov Fure funktsii kompleksnoi peremennoi v prostranstve $L_{2}(D,p(z))$”, Zhurn. vychislit. matematiki i mat. fiziki, 50:6 (2010), 999–1004 | MR | Zbl