Simply interpolating and Carleson sequences for Hardy spaces in the polydisc
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912545312342016 |
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| author | Chalmoukis, Nikolaos Dayan, Alberto |
| author_facet | Chalmoukis, Nikolaos Dayan, Alberto |
| contents | We study the relation between simply and universally interpolating sequences for the holomorphic Hardy spaces $H^p(\mathbb{D}^d)$ on the polydisc. In dimension $d=1$ a sequence is simply interpolating if and only if it is universally interpolating, due to a classical theorem of Shapiro and Shields. In dimension $d\ge2$, Amar showed that Shapiro and Shields' theorem holds for $H^p(\mathbb{D}^d)$ when $p \geq 4$. In contrast, we show that if $1\leq p \leq 2$ there exist simply interpolating sequences which are not universally interpolating. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_09099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simply interpolating and Carleson sequences for Hardy spaces in the polydisc Chalmoukis, Nikolaos Dayan, Alberto Functional Analysis Complex Variables We study the relation between simply and universally interpolating sequences for the holomorphic Hardy spaces $H^p(\mathbb{D}^d)$ on the polydisc. In dimension $d=1$ a sequence is simply interpolating if and only if it is universally interpolating, due to a classical theorem of Shapiro and Shields. In dimension $d\ge2$, Amar showed that Shapiro and Shields' theorem holds for $H^p(\mathbb{D}^d)$ when $p \geq 4$. In contrast, we show that if $1\leq p \leq 2$ there exist simply interpolating sequences which are not universally interpolating. |
| title | Simply interpolating and Carleson sequences for Hardy spaces in the polydisc |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2412.09099 |