Boundedness and Compactness of Weighted Composition Operators From Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Polydisk
In this work, we characterize the bounded and compact weighted composition operators from a large class of Banach space X of holomorphic functions on the open unit polydisk Dn into weighted-type Banach spaces of holomorphic functions on Dn. Under some restrictions on the space, we provide an approxi...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/jofs/1891869 |
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| author | Rabab Alyusof Flavia Colonna |
| author_facet | Rabab Alyusof Flavia Colonna |
| author_sort | Rabab Alyusof |
| collection | DOAJ |
| description | In this work, we characterize the bounded and compact weighted composition operators from a large class of Banach space X of holomorphic functions on the open unit polydisk Dn into weighted-type Banach spaces of holomorphic functions on Dn. Under some restrictions on the space, we provide an approximation of the essential norm of such operators. We apply our results to the cases when X is the Hardy Hilbert space, the weighted Bergman Hilbert space, a weighted-type Dirichlet space, and the Bloch space of the polydisk. |
| format | Article |
| id | doaj-art-0b63ee1fc9494fc7ad1eacaf8ffe653c |
| institution | OA Journals |
| issn | 2314-8888 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-0b63ee1fc9494fc7ad1eacaf8ffe653c2025-08-20T02:16:33ZengWileyJournal of Function Spaces2314-88882025-01-01202510.1155/jofs/1891869Boundedness and Compactness of Weighted Composition Operators From Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the PolydiskRabab Alyusof0Flavia Colonna1Department of MathematicsDepartment of Mathematical SciencesIn this work, we characterize the bounded and compact weighted composition operators from a large class of Banach space X of holomorphic functions on the open unit polydisk Dn into weighted-type Banach spaces of holomorphic functions on Dn. Under some restrictions on the space, we provide an approximation of the essential norm of such operators. We apply our results to the cases when X is the Hardy Hilbert space, the weighted Bergman Hilbert space, a weighted-type Dirichlet space, and the Bloch space of the polydisk.http://dx.doi.org/10.1155/jofs/1891869 |
| spellingShingle | Rabab Alyusof Flavia Colonna Boundedness and Compactness of Weighted Composition Operators From Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Polydisk Journal of Function Spaces |
| title | Boundedness and Compactness of Weighted Composition Operators From Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Polydisk |
| title_full | Boundedness and Compactness of Weighted Composition Operators From Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Polydisk |
| title_fullStr | Boundedness and Compactness of Weighted Composition Operators From Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Polydisk |
| title_full_unstemmed | Boundedness and Compactness of Weighted Composition Operators From Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Polydisk |
| title_short | Boundedness and Compactness of Weighted Composition Operators From Banach Spaces of Holomorphic Functions to Weighted-Type Banach Spaces on the Polydisk |
| title_sort | boundedness and compactness of weighted composition operators from banach spaces of holomorphic functions to weighted type banach spaces on the polydisk |
| url | http://dx.doi.org/10.1155/jofs/1891869 |
| work_keys_str_mv | AT rababalyusof boundednessandcompactnessofweightedcompositionoperatorsfrombanachspacesofholomorphicfunctionstoweightedtypebanachspacesonthepolydisk AT flaviacolonna boundednessandcompactnessofweightedcompositionoperatorsfrombanachspacesofholomorphicfunctionstoweightedtypebanachspacesonthepolydisk |