Geodesic
On the best simultaneous approximation of functions in the Hardy space
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 283-291 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the Hardy spaces $H_{q,\rho}$ ($1\le q\le\infty$, $0\rho\le1$), exact inequalities are found between the best simultaneous approximation of a function and the averaged moduli of smoothness of the angular boundary values of the $r$th derivatives. Some applications of these inequalities to the problem of finding the best upper bounds of the best simultaneous approximations of some classes of functions defined by moduli of smoothness and belonging to the Hardy space $H_{q,\rho}$ are given.
Keywords: best simultaneous approximation, Hardy space, upper bound, modulus of smoothness
Mots-clés : majorant. 
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M. Sh. Shabozov. On the best simultaneous approximation of functions in the Hardy space. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 283-291. http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a23/

[1] Babenko K.I., “O nailuchshikh priblizheniyakh odnogo klassa analiticheskikh funktsii”, Izv. AN SSSR. Ser. matematicheskaya, 22:5 (1958), 631–640 | Zbl

[2] Taikov L.V., “O nailuchshem priblizhenii v srednem nekotorykh klassov funktsii”, Mat. zametki, 1:2 (1967), 155–162 | MR | Zbl

[3] Taikov L.V., “Poperechniki nekotorykh klassov analiticheskikh funktsii”, Mat. zametki, 22:2 (1977), 285–295 | MR | Zbl

[4] Ainulloev N., Taikov L.V., “Nailuchshee priblizhenie v smysle A. N. Kolmogorova klassov analiticheskikh v edinichnom kruge funktsii”, Mat. zametki, 40:3 (1986), 341–351 | MR

[5] Vakarchuk S.B., “Nailuchshie lineinye metody priblizheniya i poperechniki klassov analiticheskikh v kruge funktsii”, Mat. zametki, 57:1 (1995), 30–39 | MR

[6] Vakarchuk S.B., Zabutnaya V.I., “O nailuchshikh lineinykh metodakh priblizheniya funktsii klassov L. V. Taikova v prostranstvakh Khardi $H_{q,\rho},\,q\ge1,\,0\rho\le1$”, Mat. zametki, 85:3 (2009), 323–329 | DOI | MR | Zbl

[7] Shabozov M.Sh., Shabozov O.Sh., “Poperechniki nekotorykh klassov analiticheskikh funktsii v prostranstve Khardi $ H_2$”, Mat. zametki, 68:5 (2000), 796–800 | DOI | MR | Zbl

[8] Shabozov M.Sh., Yusupov G.A., “Nailuchshee priblizhenie i znacheniya poperechnikov nekotorykh klassov analiticheskikh funktsii”, Dokl. RAN, 382:6 (2002), 747–749 | MR | Zbl

[9] Shabozov M.Sh., Yusupov G.A., Zargarov Dzh.Dzh., “O nailuchshei sovmestnoi polinomialnoi approksimatsii funktsii i ikh proizvodnykh v prostranstve Khardi”, Tr. In-ta matematiki i mekhaniki UrO RAN, 27:4 (2021), 239–254 | DOI | MR

[10] Privalov I.I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M., 1950, 336 pp.

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

[12] Vakarchuk S.B., Vakarchuk M.B., “Neravenstva tipa Kolmogorova dlya analiticheskikh funktsii odnoi i dvukh kompleksnykh peremennykh i ikh prilozhenie k teorii approksimatsii”, Ukr. mat. zhurn., 63:12 (2011), 1579–1601

[13] Zigmund A., Trigonometricheskie ryady, v 2 t., v. 1, Mir, M., 1965, 616 pp. | MR