On a conjecture about generalized integration operators on Hardy spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866916265704030208 |
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| author | Yang, Rong Li, Songxiao |
| author_facet | Yang, Rong Li, Songxiao |
| contents | A conjecture posed by Chalmoukis in 2020 states that if $T_{g,a}:H^p\to H^q(0<q<p<\infty)$ is bounded, then $g$ must be in $H^{\frac{pq}{p-q}}$. In this article, we provide a positive answer to the aforementioned conjecture. We also consider the compactness of $T_{g,a}:H^p\to H^q(0<q<p<\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a conjecture about generalized integration operators on Hardy spaces Yang, Rong Li, Songxiao Functional Analysis A conjecture posed by Chalmoukis in 2020 states that if $T_{g,a}:H^p\to H^q(0<q<p<\infty)$ is bounded, then $g$ must be in $H^{\frac{pq}{p-q}}$. In this article, we provide a positive answer to the aforementioned conjecture. We also consider the compactness of $T_{g,a}:H^p\to H^q(0<q<p<\infty)$. |
| title | On a conjecture about generalized integration operators on Hardy spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2405.19372 |