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 |
| _version_ | 1797894921367060480 |
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| author | S. S. Volosivets |
| author_facet | S. S. Volosivets |
| author_sort | S. S. Volosivets |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T07:18:13Z |
| format | Article |
| id | doaj.art-247cc5fe9ae64d2aada1804f436abdd6 |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-04-10T07:18:13Z |
| publishDate | 2022-03-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-247cc5fe9ae64d2aada1804f436abdd62023-02-24T20:27:32ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322022-03-0111 (29)210611810.15393/j3.art.2022.10711APPROXIMATION BY LINEAR MEANS OF FOURIER SERIES AND REALIZATION FUNCTIONALS IN WEIGHTED ORLICZ SPACESS. S. Volosivets0Saratov State UniversityUsing 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.https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=10711&lang=ruweighted orlicz spaces𝐾-functionalrealization functionalriesz-zygmund meanseuler means |
| spellingShingle | S. S. Volosivets APPROXIMATION BY LINEAR MEANS OF FOURIER SERIES AND REALIZATION FUNCTIONALS IN WEIGHTED ORLICZ SPACES Проблемы анализа weighted orlicz spaces 𝐾-functional realization functional riesz-zygmund means euler means |
| title | APPROXIMATION BY LINEAR MEANS OF FOURIER SERIES AND REALIZATION FUNCTIONALS IN WEIGHTED ORLICZ SPACES |
| title_full | APPROXIMATION BY LINEAR MEANS OF FOURIER SERIES AND REALIZATION FUNCTIONALS IN WEIGHTED ORLICZ SPACES |
| title_fullStr | APPROXIMATION BY LINEAR MEANS OF FOURIER SERIES AND REALIZATION FUNCTIONALS IN WEIGHTED ORLICZ SPACES |
| title_full_unstemmed | APPROXIMATION BY LINEAR MEANS OF FOURIER SERIES AND REALIZATION FUNCTIONALS IN WEIGHTED ORLICZ SPACES |
| title_short | APPROXIMATION BY LINEAR MEANS OF FOURIER SERIES AND REALIZATION FUNCTIONALS IN WEIGHTED ORLICZ SPACES |
| title_sort | approximation by linear means of fourier series and realization functionals in weighted orlicz spaces |
| topic | weighted orlicz spaces 𝐾-functional realization functional riesz-zygmund means euler means |
| url | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=10711&lang=ru |
| work_keys_str_mv | AT ssvolosivets approximationbylinearmeansoffourierseriesandrealizationfunctionalsinweightedorliczspaces |