On the relation between fourier and leont’ev coefficients with respect to smirnov spaces
Yu. Mel’nik showed that the Leont’ev coefficients Κ f (λ) in the Dirichlet series \({{2n} \mathord{\left/ {\vphantom {{2n} {\left( {n + 1} \right) < p < 2}}} \right. \kern-0em} {\left( {n + 1} \right) < p > 2}}\) of a function f ∈E p (D), 1 < p < ∞, ar...
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| Datum: | 2004 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3773 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509905982586880 |
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| author | Forster, B. Фостер, Б. |
| author_facet | Forster, B. Фостер, Б. |
| author_sort | Forster, B. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:08:07Z |
| description | Yu. Mel’nik showed that the Leont’ev coefficients Κ f (λ) in the Dirichlet series \({{2n} \mathord{\left/ {\vphantom {{2n} {\left( {n + 1} \right) < p < 2}}} \right. \kern-0em} {\left( {n + 1} \right) < p > 2}}\) of a function f ∈E p (D), 1 < p < ∞, are the Fourier coefficients of some function F ∈L p , ([0, 2π]) and that the first modulus of continuity of F can be estimated by the first moduli and majorants in f. In the present paper, we extend his results to moduli of arbitrary order. |
| first_indexed | 2026-03-24T02:48:32Z |
| format | Article |
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| id | umjimathkievua-article-3773 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:48:32Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/df/86df5efe31fe1982c8da9fa47a359adf.pdf |
| spelling | umjimathkievua-article-37732020-03-18T20:08:07Z On the relation between fourier and leont’ev coefficients with respect to smirnov spaces Про співвідношення між коефіцієнтами Фур'є та Леонтьєва стосовно просторів Смірнова Forster, B. Фостер, Б. Yu. Mel’nik showed that the Leont’ev coefficients Κ f (λ) in the Dirichlet series \({{2n} \mathord{\left/ {\vphantom {{2n} {\left( {n + 1} \right) < p < 2}}} \right. \kern-0em} {\left( {n + 1} \right) < p > 2}}\) of a function f ∈E p (D), 1 < p < ∞, are the Fourier coefficients of some function F ∈L p , ([0, 2π]) and that the first modulus of continuity of F can be estimated by the first moduli and majorants in f. In the present paper, we extend his results to moduli of arbitrary order. Ю. І. Мельник показав, що коефіцієнти Леонтьєва \({{2n} \mathord{\left/ {\vphantom {{2n} {\left( {n + 1} \right) < p < 2}}} \right. \kern-0em} {\left( {n + 1} \right) < p > 2}}\) для функції f ∈E p (D), 1 < p < ∞, є коефіцієнтами Фур'є для деякої функції $F\in L^p, ([0, 2π])$ і що перший модуль неперервності $F$ можна оцінити першими модулями та мажораптами в f. У даній статті його результати поширено на модулі довільного порядку. Institute of Mathematics, NAS of Ukraine 2004-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3773 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 4 (2004); 517–526 Український математичний журнал; Том 56 № 4 (2004); 517–526 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/3773/4268 https://umj.imath.kiev.ua/index.php/umj/article/view/3773/4269 Copyright (c) 2004 Forster B. |
| spellingShingle | Forster, B. Фостер, Б. On the relation between fourier and leont’ev coefficients with respect to smirnov spaces |
| title | On the relation between fourier and leont’ev coefficients with respect to smirnov spaces |
| title_alt | Про співвідношення між коефіцієнтами Фур'є та Леонтьєва стосовно просторів Смірнова |
| title_full | On the relation between fourier and leont’ev coefficients with respect to smirnov spaces |
| title_fullStr | On the relation between fourier and leont’ev coefficients with respect to smirnov spaces |
| title_full_unstemmed | On the relation between fourier and leont’ev coefficients with respect to smirnov spaces |
| title_short | On the relation between fourier and leont’ev coefficients with respect to smirnov spaces |
| title_sort | on the relation between fourier and leont’ev coefficients with respect to smirnov spaces |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3773 |
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