On the Cesàro operator in the Hardy space in the upper half plane
UDC 517.9 We consider the Cesàro operator in the Hardy space in the upper half plane. We provide a new simple proof of boundedness of this operator and show that this operator is equal to the sum of the identity operator and a unitary operator, which implies its normality.
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| Date: | 2026 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8523 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513150068064256 |
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| author | Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. |
| author_facet | Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. |
| author_sort | Andreev, Valentin V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:39:33Z |
| description | UDC 517.9
We consider the Cesàro operator in the Hardy space in the upper half plane. We provide a new simple proof of boundedness of this operator and show that this operator is equal to the sum of the identity operator and a unitary operator, which implies its normality. |
| doi_str_mv | 10.3842/umzh.v77i6.8523 |
| first_indexed | 2026-03-24T03:40:06Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8523 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:40:06Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-85232026-03-21T13:39:33Z On the Cesàro operator in the Hardy space in the upper half plane On the Cesàro operator in the Hardy space in the upper half plane Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. Cesàro operator, Hardy space, reproducing kernel, unitary operator. UDC 517.9 We consider the Cesàro operator in the Hardy space in the upper half plane. We provide a new simple proof of boundedness of this operator and show that this operator is equal to the sum of the identity operator and a unitary operator, which implies its normality. УДК 517.9 Про оператор Чезаро у просторі Гарді у верхній півплощині Розглянуто оператор Чезаро у просторі Гарді у верхній півплощині. Наведено нове просте доведення обмеженості цього оператора, а також встановлено, що він є сумою тотожного та унітарного операторів, що, зокрема, означає його нормальність. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8523 10.3842/umzh.v77i6.8523 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 6 (2025); 441–442 Український математичний журнал; Том 77 № 6 (2025); 441–442 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8523/10535 Copyright (c) 2025 Valentin V. Andreev, Miron B. Bekker, Joseph A. Cima |
| spellingShingle | Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. On the Cesàro operator in the Hardy space in the upper half plane |
| title | On the Cesàro operator in the Hardy space in the upper half plane |
| title_alt | On the Cesàro operator in the Hardy space in the upper half plane |
| title_full | On the Cesàro operator in the Hardy space in the upper half plane |
| title_fullStr | On the Cesàro operator in the Hardy space in the upper half plane |
| title_full_unstemmed | On the Cesàro operator in the Hardy space in the upper half plane |
| title_short | On the Cesàro operator in the Hardy space in the upper half plane |
| title_sort | on the cesàro operator in the hardy space in the upper half plane |
| topic_facet | Cesàro operator Hardy space reproducing kernel unitary operator. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8523 |
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