On the boundedness of generalized integration operators on Hardy spaces
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914829080461312 |
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| author | Chalmoukis, Nikolaos Nikolaidis, Georgios |
| author_facet | Chalmoukis, Nikolaos Nikolaidis, Georgios |
| contents | We study the boundedness and compactness properties of the generalized integration operator $T_{g,a}$ when it acts between distinct Hardy spaces in the unit disc of the complex plane. This operator has been introduced by the first author in connection to a theorem of Cohn about factorization of higher order derivatives of functions in Hardy spaces. We answer in the affirmative a conjecture stated in the same work, therefore giving a complete characterization of the class of symbols $g$ for which the operator is bounded from the Hardy space $H^p$ to $H^q, \, 0<p,q<\infty.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13920 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the boundedness of generalized integration operators on Hardy spaces Chalmoukis, Nikolaos Nikolaidis, Georgios Complex Variables Functional Analysis Primary: 30H10, Secondary 30H30, 47G10 We study the boundedness and compactness properties of the generalized integration operator $T_{g,a}$ when it acts between distinct Hardy spaces in the unit disc of the complex plane. This operator has been introduced by the first author in connection to a theorem of Cohn about factorization of higher order derivatives of functions in Hardy spaces. We answer in the affirmative a conjecture stated in the same work, therefore giving a complete characterization of the class of symbols $g$ for which the operator is bounded from the Hardy space $H^p$ to $H^q, \, 0<p,q<\infty.$ |
| title | On the boundedness of generalized integration operators on Hardy spaces |
| topic | Complex Variables Functional Analysis Primary: 30H10, Secondary 30H30, 47G10 |
| url | https://arxiv.org/abs/2405.13920 |