Abstract:
In the Hardy spaces Hq,ρ (1⩽q⩽∞, 0<ρ⩽1), 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 rth 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 Hq,ρ are given.
Keywords:
best simultaneous approximation, Hardy space, upper bound, modulus of smoothness, majorant.
Citation:
M. Sh. Shabozov, “On the best simultaneous approximation of functions in the Hardy space”, Trudy Inst. Mat. i Mekh. UrO RAN, 29, no. 4, 2023, 283–291
\Bibitem{Sha23}
\by M.~Sh.~Shabozov
\paper On the best simultaneous approximation of functions in the Hardy space
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2023
\vol 29
\issue 4
\pages 283--291
\mathnet{http://mi.mathnet.ru/timm2055}
\crossref{https://doi.org/10.21538/0134-4889-2023-29-4-283-291}
\elib{https://elibrary.ru/item.asp?id=54950415}
\edn{https://elibrary.ru/adehng}
Linking options:
https://www.mathnet.ru/eng/timm2055
https://www.mathnet.ru/eng/timm/v29/i4/p283
This publication is cited in the following 3 articles:
M. Sh. Shabozov, R. A. Karimzoda, “$\mathcal{K}$-funktsionaly i tochnye znacheniya $n$-poperechnikov
nekotorykh klassov funktsii v prostranstve Xardi”, Tr. IMM UrO RAN, 30, no. 4, 2024, 301–308
Mirgand Sh. Shabozov, Muqim S. Saidusajnov, “On widths of some classes of analytic functions in a circle”, Ural Math. J., 10:2 (2024), 121–130
M. Sh. Shabozov, A. A. Shabozova, “O tochnykh znacheniyakh poperechnikov klassov analiticheskikh v kruge funktsii”, Matem. tr., 27:4 (2024), 115–140
Citation in format AMSBIB
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