APPROXIMATION BY LINEAR MEANS OF FOURIER SERIES AND REALIZATION FUNCTIONALS IN WEIGHTED ORLICZ SPACES
Using one-sided Steklov means, we introduce a new modulus of smoothness in weighted Orlicz spaces and state its equivalence with a special 𝐾-functional. We prove Stechkin-Nikol’skii-type inequality for trigonometric polynomials and direct estimates for the approximation by Riesz-Zygmund, Vall´ee-P...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2022-03-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=10711&lang=ru |
| Summary: | Using one-sided Steklov means, we introduce a new
modulus of smoothness in weighted Orlicz spaces and state its
equivalence with a special 𝐾-functional. We prove Stechkin-Nikol’skii-type inequality for trigonometric polynomials and direct estimates for the approximation by Riesz-Zygmund, Vall´ee-Poussin,
and Euler means in weighted Orlicz spaces. By these results, several types of realization functionals equivalent to the above cited
𝐾-functional in points 1/𝑛, 𝑛 ∈ N, are constructed. |
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| ISSN: | 2306-3424 2306-3432 |