Carleson measures on Hardy spaces with bicomplex scalars
UDC 517.53 We explore Carleson measures given on the Hardy spaces defined over the bicomplex space and investigate the properties of the bicomplex Toeplitz operator. In the first section, we provide a comprehensive introduction and formulate the key definitions necessary for the subsequent analysis....
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| Datum: | 2026 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8614 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513194658758656 |
|---|---|
| author | Dolkar, Stanzin Kumar, Sanjay Dolkar, Stanzin Kumar, Sanjay |
| author_facet | Dolkar, Stanzin Kumar, Sanjay Dolkar, Stanzin Kumar, Sanjay |
| author_sort | Dolkar, Stanzin |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T11:04:14Z |
| description | UDC 517.53
We explore Carleson measures given on the Hardy spaces defined over the bicomplex space and investigate the properties of the bicomplex Toeplitz operator. In the first section, we provide a comprehensive introduction and formulate the key definitions necessary for the subsequent analysis. In the second section, we present the results for $\mathbb{D}$-Carleson measures and establish their relationship with bicomplex Hardy spaces. Finally, in the last section, we extend the concept of the Toeplitz operator to the bicomplex space, thus offering broader prospects. |
| doi_str_mv | 10.3842/umzh.v78i1-2.8614 |
| first_indexed | 2026-03-24T03:40:48Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8614 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:40:48Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-86142026-03-21T11:04:14Z Carleson measures on Hardy spaces with bicomplex scalars Carleson measures on Hardy spaces with bicomplex scalars Dolkar, Stanzin Kumar, Sanjay Dolkar, Stanzin Kumar, Sanjay Bicomplex numbers, Carleson measures, Hardy spaces, Holomorphic functions 30G35, 32A30, 32A10 UDC 517.53 We explore Carleson measures given on the Hardy spaces defined over the bicomplex space and investigate the properties of the bicomplex Toeplitz operator. In the first section, we provide a comprehensive introduction and formulate the key definitions necessary for the subsequent analysis. In the second section, we present the results for $\mathbb{D}$-Carleson measures and establish their relationship with bicomplex Hardy spaces. Finally, in the last section, we extend the concept of the Toeplitz operator to the bicomplex space, thus offering broader prospects. УДК 517.53 Карлесонові міри на просторах Гарді з бікомплексними скалярами Розглянуто карлесонові міри, визначені на просторах Гарді над бікомплексним простором, та досліджено властивості бікомплексного оператора Тепліца. У першому розділі подано розгорнуту вступну частину та наведено основні означення необхідні для подальшого аналізу. У другому розділі отримано результати щодо $\mathbb{D}$-карлесонових мір і їхнього зв'язку з бікомплексними просторами Гарді. В останньому розділі узагальнено поняття оператора Тепліца на бікомплексний простір, що забезпечує ширші перспективи подальших дослідження. Institute of Mathematics, NAS of Ukraine 2026-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8614 10.3842/umzh.v78i1-2.8614 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 1-2 (2026); 82 Український математичний журнал; Том 78 № 1-2 (2026); 82 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8614/10622 Copyright (c) 2026 Stanzin Dolkar, Sanjay Kumar |
| spellingShingle | Dolkar, Stanzin Kumar, Sanjay Dolkar, Stanzin Kumar, Sanjay Carleson measures on Hardy spaces with bicomplex scalars |
| title | Carleson measures on Hardy spaces with bicomplex scalars |
| title_alt | Carleson measures on Hardy spaces with bicomplex scalars |
| title_full | Carleson measures on Hardy spaces with bicomplex scalars |
| title_fullStr | Carleson measures on Hardy spaces with bicomplex scalars |
| title_full_unstemmed | Carleson measures on Hardy spaces with bicomplex scalars |
| title_short | Carleson measures on Hardy spaces with bicomplex scalars |
| title_sort | carleson measures on hardy spaces with bicomplex scalars |
| topic_facet | Bicomplex numbers Carleson measures Hardy spaces Holomorphic functions 30G35 32A30 32A10 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8614 |
| work_keys_str_mv | AT dolkarstanzin carlesonmeasuresonhardyspaceswithbicomplexscalars AT kumarsanjay carlesonmeasuresonhardyspaceswithbicomplexscalars AT dolkarstanzin carlesonmeasuresonhardyspaceswithbicomplexscalars AT kumarsanjay carlesonmeasuresonhardyspaceswithbicomplexscalars |