On integral representations in the Hardi classes and on the best approximations in some functional spaces
For the case of a simply connected domain in the plane one proves necessary and sufficient conditions for the representation of functions of the Hardy class $H^1$ by an integral with respect to the harmonic measure of its boundary values. A theorem is given, characterizing the rate of decrease of th...
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| Date: | 1991 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1991
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9613 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865795320455102464 |
|---|---|
| author | Dovgoshei , A. A. Довгошей , А. А. |
| author_facet | Dovgoshei , A. A. Довгошей , А. А. |
| author_institution_txt_mv | [
{
"author": "А. А. Довгошей ",
"institution": "Ин-т прикл. математики и механики АН УССР, Донецк"
}
] |
| author_sort | Dovgoshei , A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-10-09T12:05:28Z |
| description | For the case of a simply connected domain in the plane one proves necessary and sufficient conditions for the representation of functions of the Hardy class $H^1$ by an integral with respect to the harmonic measure of its boundary values. A theorem is given, characterizing the rate of decrease of the best polynomial approximations of an entire function in Hardy classes by the order and the type of this function. |
| first_indexed | 2026-03-24T03:46:13Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9613 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:46:13Z |
| publishDate | 1991 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-96132025-10-09T12:05:28Z On integral representations in the Hardi classes and on the best approximations in some functional spaces Об интегральных представлениях в классах Харди и наилучших приближениях в некоторых функциональных пространствах Dovgoshei , A. A. Довгошей , А. А. - For the case of a simply connected domain in the plane one proves necessary and sufficient conditions for the representation of functions of the Hardy class $H^1$ by an integral with respect to the harmonic measure of its boundary values. A theorem is given, characterizing the rate of decrease of the best polynomial approximations of an entire function in Hardy classes by the order and the type of this function. Для случая односвязной ограниченной области на плоскости доказываются необходимые и достаточные условия для представления функций класса Харди $H^1$ интегралом по гармонической мере от своих граничных значений. Приведена теорема, характеризующая скорость убывания наилучших полиномиальных приближений целой функции в классах Харди через порядок II тип этой функции. Для випадку однозв’язної обмеженої області на площині встановлені необхідні і достатні умови зображення функцій класу Харді $H^1$ інтегралом по гармонічній мірі від своїх граничних значень. Наведено теорему, що характеризує швидкість спадання найкращих поліноміальних наближень цілої функції в класах Харді через порядок і тип цієї функції. Institute of Mathematics, NAS of Ukraine 1991-02-28 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9613 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 3 (1991); 342-347 Український математичний журнал; Том 43 № 3 (1991); 342-347 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9613/10581 Copyright (c) 1991 А. А. Довгошей |
| spellingShingle | Dovgoshei , A. A. Довгошей , А. А. On integral representations in the Hardi classes and on the best approximations in some functional spaces |
| title | On integral representations in the Hardi classes and on the best approximations in some functional spaces |
| title_alt | Об интегральных представлениях в классах Харди и наилучших приближениях в некоторых функциональных пространствах |
| title_full | On integral representations in the Hardi classes and on the best approximations in some functional spaces |
| title_fullStr | On integral representations in the Hardi classes and on the best approximations in some functional spaces |
| title_full_unstemmed | On integral representations in the Hardi classes and on the best approximations in some functional spaces |
| title_short | On integral representations in the Hardi classes and on the best approximations in some functional spaces |
| title_sort | on integral representations in the hardi classes and on the best approximations in some functional spaces |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9613 |
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