On estimates of the approximation of functions from a symmetric space by Fourier sums in the uniform metric
ОБ ОЦЕНКАХ ПРИБЛИЖЕНИЯ ФУНКЦИИ ИЗ СИММЕТРИЧНОГО ПРОСТРАНСТВА СУММАМИ ФУРЬЕ В РАВНОМЕРНОЙ МЕТРИКЕ
Akishev G.
2024Krasovskii Institute of Mathematics and Mechanics
Trudy Instituta Matematiki i Mekhaniki UrO RAN
2024#30Issue 49 - 26 pp.
The article discusses the symmetric space of periodic functions of several variables, specifically, the generalized Lorentz–Zygmund space and the Nikol’skii–Besov class within this space. Estimates for the approximation of functions from the Nikol’skii–Besov class by partial sums over step hyperbolic crosses of Fourier series are established in the uniform metric. An analog of the Jackson–Nikol’skii inequality for multiple trigonometric polynomials in the norms of the generalized Lorentz–Zygmund space and the space of continuous functions is proved.
Fourier sum , Lorentz–Zygmund space , Nikol’skii–Besov class , symmetric space
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Lomonosov Moscow University, Kazakhstan Branch, Astana, 010010, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Lomonosov Moscow University
Institute of Mathematics and Mathematical Modeling
10 лет помогаем публиковать статьи Международный издатель
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