Аннотация:
Using one-sided Steklov means, we introduce a new modulus of smoothness in weighted Orlicz spaces and state its equivalence with a special KK-functional. We prove Stechkin-Nikol'skii-type inequality for trigonometric polynomials and direct estimates for the approximation by Riesz-Zygmund, Vallée-Poussin, and Euler means in weighted Orlicz spaces. By these results, several types of realization functionals equivalent to the above cited KK-functional in points 1/n1/n, n∈N, are constructed.
Supported by the Ministry of science and education of the Russian Federation in the framework of the basic part of the scientific research state task, project FSRR-2020-0006.
Поступила в редакцию: 09.08.2021 Исправленный вариант: 06.01.2022 Принята в печать: 02.02.2022
Образец цитирования:
S. S. Volosivets, “Approximation by linear means of Fourier series and realization functionals in weighted Orlicz spaces”, Пробл. анал. Issues Anal., 11(29):2 (2022), 106–118
\RBibitem{Vol22}
\by S.~S.~Volosivets
\paper Approximation by linear means of Fourier series and realization functionals in weighted Orlicz spaces
\jour Пробл. анал. Issues Anal.
\yr 2022
\vol 11(29)
\issue 2
\pages 106--118
\mathnet{http://mi.mathnet.ru/pa355}
\crossref{https://doi.org/10.15393/j3.art.2022.10711}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4459170}
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https://www.mathnet.ru/rus/pa355
https://www.mathnet.ru/rus/pa/v29/i2/p106
Эта публикация цитируется в следующих 2 статьяx:
Sadulla Jafarov, “Trigonometric approximation of periodic functions in Morrey spaces using matrix means of their Fourier series”, Mathematica Moravica, 28:2 (2024), 45
H. Kalita, “The weak drop property and the de la Vallée Poussin Theorem”, Пробл. анал. Issues Anal., 12(30):3 (2023), 105–118
Цитирование в формате AMSBIB
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